GRK 1529:  Mathematical Fluid Dynamics

• Subject Area: Mathematics
• Term: from 2009 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 69014896

• Final Report Year: 2018

Final Report Abstract

In modern mathematical fluid dynamics, fundamental well-posedness questions for viscous and inviscid fluids as well as more applied topics such as vorticity behavior, boundary layers and free boundary value problems for Newtonian, complex as well as for geophysical fluids play a dominant role. The rigorous mathematical treatment of the underlying structures requires novel concepts and methods from various disciplines in mathematics ranging from modeling, analysis and stochastics over numerics, optimization and inverse problems up to the theory of computability and complexity. The IRTG 1529 aimed to examine the mathematical structures of the underlying equations and to apply the results to various models describing e.g. geophysical flows, fluid mixtures, hydrodynamic limits, and free or moving boundary value problems for complex fluids. Major contributions to these problems are due to the principal investigators from Waseda University, University of Tokyo and TU Darmstadt. Students with a thorough background in at least one of the fields of analysis, stochastics, modeling, complexity and computablity theory, numerics, sceintific computation or optimization received an interdisciplinary education in key areas of mathematical fluid dynamics, enabling them to successfully pursue research on problems, which without our common study program and without the cooperation with our Japanese partners would have been much more difficult or even impossible to handle. The yearlong interdisciplinary course, and later on special courses and seminars taught jointly by our German-Japanese team, provided students with one common scientific language in fluid dynamics. This broad but nevertheless focused education was needed to successfully treat our scientific projects. The research of our students was guided by an advisor and co-advisors in Darmstadt and Tokyo. Students from Darmstadt were requested to spend at least 6 months in Tokyo working there with their coadvisor. Due to this international component, the scientific visibility of the PhDs was certainly a high one. IRTG 1529 was embedded in a very active and well established research environment in Darmstadt and its counterparts in Tokyo. Our extensive conference and guest programs exposed our students to latest research results and gave them the opportunity to interact with leading experts already at an early stage of their projects. Special courses or tutorials were often embedded into workshops or conferences organized by IRTG 1529. The combiniation between tutorials and the presentation of prevailing research results within workshops was very sucessful and ensured that almost all of our doctoral students completed their PhD within 3 years. After a thesis written by an IRTG student was submitted to the Department of Mathematics at TU Darmstadt, the thesis committee needed to require at least one official report on this thesis by the Japanese co-advisor of this student. His judgement including his grade were taken into account with equal weight as the other reports. The scientific output of all projects includes in total 410 publications in refereed journals, in particular 287 publications, often in excellent journals, authored or coauthored by students or postdocs inside IRTG 1529 funded by DFG and JSPS and 73 joint German-Japanese publications, also often in excellent journals, authored or coauthored by students, postdocs or professors inside IRTG 1529 and funded by DFG or JSPS.

Publications

• Local existence and blow-up criterion for the Euler equations in Besov spaces of weak type, J. E Equ., 8, (2008), 693–725
  R. Takada
  (See online at https://doi.org/10.1007/s00028-008-0403-6)
• A continuous adjoint approach to shape optimization for Navier-Stokes flow, Optimal control of coupled systems of partial differential equations, International Series of Numerical Mathematics, Birkhäuser, 158, (2009), 35–56
  C. Brandenburg, F. Lindemann, M. Ulbrich, S. Ulbrich
  (See online at https://doi.org/10.1007/978-3-7643-8923-9_2)
• Asymptotic profiles of steady Stokes and Navier-Stokes flows around a rotating obstacle, Ann. Univ. Ferrera, 55, (2009), 263–277
  R. Farwig, T. Hishida
  (See online at https://doi.org/10.1007/s11565-009-0072-6)
• Difference approximation to Aubry-Mather sets, RIMS Kôkyûroku, Kyoto University, 1688, (2009), 7-19
  K. Soga
  
• Energy-based regularity criteria for the Navier-Stokes equations, J. Math. Fluid Mech., 11, (2009), 428–442
  R. Farwig, H. Kozono, H. Sohr
  (See online at https://doi.org/10.1007/s00021-008-0267-0)
• Finite-type invariants for curves on surfaces, Proc. Japan Acad. Ser. A Math. Sci., 85, (2009), 129–134
  N. Ito
  (See online at https://doi.org/10.3792/pjaa.85.129)
• On the Lp − Lq maximal regularity for the linear thermoelastic plate equation in a bounded domain, Math. Methods Appl. Sci., 32, (2009), no. 13, 1609–1637
  Y. Naito
  (See online at https://doi.org/10.1002/mma.1100)
• On the Lpp analytic semigroup associated with the linear thermoelastic plate equations in the half-space, J. Math. Soc. Japan, 61, (2009), no. 4, 971–1011
  Y. Naito, Y. Shibata
  (See online at https://doi.org/10.2969/jmsj/06140971)
• On the Stokes operator in general unbounded domains, Hokkaido Math. J., 38, (2009), 111–136
  R. Farwig, H. Kozono, H. Sohr
  (See online at https://doi.org/10.14492/hokmj/1248787007)
• Periodic solutions of the forced Burgers equation, RIMS Kôkyûroku, 1631, (2009), 147–159
  T. Nishida, K. Soga
  
• Stability of plane Couette flows with respect to small periodic perturbations, Nonlinear Anal., 71, (2009), 3739–3758
  H. Heck, H. Kim, H. Kozono
  (See online at https://doi.org/10.1016/j.na.2009.02.034)
• Uniqueness of Positive Solutions for a Nonlinear Elliptic System, NoDEA, 16, (2009), 555–567
  N. Ikoma
  (See online at https://doi.org/10.1007/s00030-009-0017-x)
• A point-wise criterion for quasi-periodic motions in the KAM theory, Nonlinear Analysis, 73, (2010), 3151-3161
  K. Soga
  (See online at https://doi.org/10.1016/j.na.2010.06.058)
• Asymptotic behaviors and classical limits of solutions to a quantum drift-diffusion model for semiconductors, Math. Models Methods Appl. Sci., 20, (2010), 909–936
  S. Nishibata, N. Shigeta, M. Suzuki
  (See online at https://doi.org/10.1142/S0218202510004477)
• Asymptotic stability of stationary solutions to the Euler-Poisson equations arising in plasma physics, Kinet. Relat. Models, 4, (2010), 569–588
  M. Suzuki
  (See online at https://doi.org/10.3934/krm.2011.4.569)
• Construction of invariants of curves and fronts using word theory, J. Knot Theory Ramifications, 19, (2010), 1205–1245
  N. Ito
  (See online at https://doi.org/10.1142/S0218216510008406)
• Counterexamples of commutator estimates in the Besov and the Triebel-Lizorkin spaces related to the Euler equations, SIAM J. Math. Anal., 42, (2010), 2473–2483
  R. Takada
  (See online at https://doi.org/10.1137/100782498)
• Existence of standing waves for coupled nonlinear Schrödinger equations, Tokyo J. Math., 33, (2010), 89–116
  N. Ikoma
  (See online at https://doi.org/10.3836/tjm/1279719580)
• Global weak solutions of the Navier-Stokes system with nonzero boundary conditions, Funkcialaj Ekvacioj, 53, (2010), 231–247
  R. Farwig, H. Kozono, H. Sohr
  (See online at https://doi.org/10.1619/fesi.53.231)
• Low frequency expansion in thermoelasticity with second sound in three dimensions, J. Math. Soc. Japan, 62, (2010), 1289–1316
  Y. Naito, R. Racke, Y. Shibata
  (See online at https://doi.org/10.2969/jmsj/06241289)
• Non-existence of finite-time self-similar solutions of the Keller-Segel system in the scaling invariant class, J. Math. Anal. Appl., 365, (2010), 60–66
  H. Kozono, Y. Sugiyama, R. Takada
  (See online at https://doi.org/10.1016/j.jmaa.2009.09.063)
• Nonlinear Partial Differential Equations. Progress in Nonlinear Differential Equations and their Applications, 79, Birkhauser Boston, 2010
  M.-H. Giga, Y. Giga, and J. Saal
  (See online at https://doi.org/10.1007/978-0-8176-4651-6)
• Nonlinear scalar field equations in RN : mountain pass and symmetric mountain pass approaches, Topol. Methods Nonlinear Anal., 35, (2010), 253–276
  J. Hirata, N. Ikoma, K. Tanaka
  
• On quasilinear parabolic evolution equations in weighted Lp-spaces, J. Evol. Equ., 10, (2010), no. 2, 443–463
  M. Köhne, J. Prüss, M. Wilke
  (See online at https://doi.org/10.1007/s00028-010-0056-0)
• On the energy equality of Navier-Stokes equations in general domains, Arch. Math., 95, (2010), 447–456
  R. Farwig, Y. Taniuchi
  (See online at https://doi.org/10.1007/s00013-010-0187-0)
• Periodic solutions of the Navier-Stokes equations with inhomogeneous boundary conditions, Ann. Univ. Ferrara Sez. VII Sci. Mat., 56, (2010), 249–281
  R. Farwig, T. Okabe
  (See online at https://doi.org/10.1007/s11565-010-0108-y)
• Periodic solutions of the Navier-Stokes equations with inhomogeneous boundary conditions, Ann. Univ. Ferrara Sez. VII Sci. Mat., 56, (2010), 249–281
  R. Farwig, T. Okabe
  (See online at https://doi.org/10.1007/s11565-010-0108-y)
• Regularity of weak solutions for the Navier-Stokes system via energy criteria, In: Adv. Math. Fluid Mech., Springer, (2010), 215—227
  R. Farwig, H. Kozono, H. Sohr
  (See online at https://doi.org/10.1007/978-3-642-04068-9_13)
• Relaxation limit and initial layer to hydrodynamic models for semiconductors, J. Differential Equations, 249, (2010), 1385–1409
  S. Nishibata, M. Suzuki
  (See online at https://doi.org/10.1016/j.jde.2010.06.008)
• Remarks on the Lp-approach to the Stokes equation on unbounded domains, Discrete Contin. Dyn. Syst. Ser. S, 3, (2010), 291–297
  M. Geissert, H. Heck, M. Hieber, O. Sawada
  (See online at https://doi.org/10.3934/dcdss.2010.3.291)
• Remarks on the Lp-approach to the Stokes equation on unbounded domains, Discrete Contin. Dyn. Syst. Ser. S, 3, (2010), 291–297
  M. Geissert, H. Heck, M. Hieber, O. Sawada
  (See online at https://doi.org/10.3934/dcdss.2010.3.291)
• The Fujita-Kato approach to the Navier-Stokes equations in the rotational framework. Math. Z., 265, (2010), 481–491
  M. Hieber, Y. Shibata
  (See online at https://doi.org/10.1007/s00209-009-0525-8)
• A local mountain pass type result for a system of nonlinear Schrödinger equations, Calc. Var. Partial Differential Equations, 40, (2011), 449–480
  N. Ikoma, K. Tanaka
  (See online at https://doi.org/10.1007/s00526-010-0347-x)
• A non-autonomous model problem for the Oseen-Navier-Stokes flow with rotating effects, J. Math. Soc. Japan, 63, (2011), 1027–1037
  M. Geissert, T. Hansel
  (See online at https://doi.org/10.2969/jmsj/06331027)
• Asymptotic Behavior of a Leray Solution around a Rotating Obstacle, Progress in Nonlinear Differential Equations and Their Applications, 60, (2011), 251–266
  G. P. Galdi, M. Kyed
  (See online at https://doi.org/10.1007/978-3-0348-0075-4_13)
• Asymptotic profiles of steady Stokes and Navier-Stokes flows around a rotating obstacle. Manuscripta Math., 136, (2011), 315–338
  R. Farwig, T. Hishida
  (See online at https://doi.org/10.1007/s00229-011-0479-0)
• Asymptotic Structure of a Leray solution to the Navier-Stokes flow around a rotating body, Pacific J. Math., 253, (2011), 367–382
  R. Farwig, G.P. Galdi, M. Kyed
  (See online at https://doi.org/10.2140/pjm.2011.253.367)
• Chain homotopy maps for Khovanov homology, J. Knot Theory Ramifications, 20, (2011), 127– 139
  N. Ito
  (See online at https://doi.org/10.1142/S0218216511008656)
• Finite type invariants of nanowords and nanophrases, Topology Appl., 158, (2011), 1050–1072
  N. Ito, A. Gibson, N. Ito
  (See online at https://doi.org/10.1016/j.topol.2011.02.008)
• Global Leray-Hopf weak solutions of the Navier-Stokes equations with nonzero timedependent boundary values, In: Parabolic Problems: Progr. Nonlineear Differential Equations, 80, (2011), 211–232
  R. Farwig, H. Kozono, H. Sohr
  (See online at https://doi.org/10.1007/978-3-0348-0075-4_11)
• Global weak solutions of the Navier-Stokes system with nonhomogeneous boundary data and divergence, Rend. Semin. Mat. Univ. Padova, 125, (2011), 51–70
  R. Farwig, H. Kozono, H. Sohr
  (See online at https://doi.org/10.4171/RSMUP/125-4)
• Global well-posedness for Keller-Segel system in Besov type spaces, J. Math. Anal. Appl., 379, (2011), 930–948
  T. Iwabuchi
  (See online at https://doi.org/10.1016/j.jmaa.2011.02.010)
• Hierarchy of semiconductor equations: relaxation limits with initial layers for large initial data, MSJ Mem., 26, (2011)
  S. Nishibata, M. Suzuki (eds.)
  (See online at https://doi.org/10.1142/e028)
• Invariants of Handlebody-Knots via Yokota's Invariants
  A. Mizusawa, J. Murakami
  (See online at https://doi.org/10.48550/arXiv.1112.2719)
• L1-maximal regularity for the Laplacian and applications, Discrete Contin. Dyn. Syst., supplement, 2011, (2011), 495–504
  Y. Giga, J. Saal
  (See online at https://doi.org/10.3934/proc.2011.2011.495)
• Leading term at infinity of steady Navier-Stokes flow around a rotating obstacle, Math. Nachr., 284, (2011), 2065–2077
  R. Farwig, T. Hishida
  (See online at https://doi.org/10.1002/mana.200910192)
• Non-autonomous Ornstein-Uhlenbeck equations in exterior domains, Adv. Differential Equations, 16, (2011), no. 3-4, 201–220
  T. Hansel, A. Rhandi
  
• On the analyticity and the almost periodicity of the solution to the Euler equations with non-decaying initial velocity, J. Funct. Anal., 260, (2011), no. 7, 2148–2162
  O. Sawada, R. Takada
  (See online at https://doi.org/10.1016/j.jfa.2010.12.011)
• On the Navier-Stokes flow with rotating effect and prescribed outflow velocity, J. Math. Fluid Mech., 13, (2011), 405–419
  T. Hansel
  (See online at https://doi.org/10.1007/s00021-010-0026-x)
• Periodic solutions of the Navier-Stokes equations with the inhomogeneous time dependent boundary data under the general flux condition, J. Evol. Equ., 11, (2011), 265–286
  T. Okabe
  (See online at https://doi.org/10.1007/s00028-010-0091-x)
• Steady-state Navier-Stokes flows past a rotating body: Leray solutions are physically reasonable, Arch. Ration. Mech. Anal., 200, (2011), 21–58
  G. P. Galdi, M. Kyed
  (See online at https://doi.org/10.1007/s00205-010-0350-6)
• The Influence of frequency-limited and noise-contaminated sensing on reactive turbulence control schemes, Seventh International Symposium on Turbulence and Shear Flows, (2011)
  A. Stroh, B. Frohnapfel, Y. Hasegawa, N. Kasagi, C. Tropea
  
• The Influence of frequency-limited and noise-contaminated sensing on reactive turbulence control schemes, Seventh International Symposium on Turbulence and Shear Flows, (2011)
  A. Stroh, B. Frohnapfel, Y. Hasegawa, N. Kasagi, C. Tropea
  
• The spin-coating process: analysis of the free boundary value problem, Comm. Partial Differential Equations, 36, (2011), no. 7, 1145–1192
  R. Denk, M. Geissert, M. Hieber, J. Saal, O. Sawada
  (See online at https://doi.org/10.1080/03605302.2010.546469)
• The spin-coating process: analysis of the free boundary value problem, Comm. Partial Differential Equations, 36, (2011), no. 7, 1145–1192
  R. Denk, M. Geissert, M. Hieber, J. Saal, O. Sawada
  (See online at https://doi.org/10.1080/03605302.2010.546469)
• Uniqueness of almost periodic-in-time solutions to Navier-Stokes equations in unbounded domains, J. Evol. Equ., 11, (2011), 485–500
  R. Farwig, Y. Taniuchi
  (See online at https://doi.org/10.1007/s00028-010-0098-3)
• Weak solutions of the Navier-Stokes system with nonzero boundary values in an exterior domain, In: Math. Analysis of the Navier-Stokes equations and related topics, past and future, Gakuto, Tokyo, 35, (2011), 31–52
  R. Farwig, H. Kozono, F. Riechwald
  
• A description of Bourgain-Pavlovíc’s ill-posedness theorem of the Navier-Stokes equations in the critical Besov space, Harmonic analysis and nonlinear partial differential equations, RIMS Kôkyûroku Bessatsu, B33, Res. Inst. Math. Sci. (RIMS), Kyoto, (2012), 59–85
  O. Sawada
  
• An approach to rotating boundary layers based on vector radon measures, J. Math. Fluid Mech., (2012), 1–39
  Y. Giga, J. Saal
  (See online at https://doi.org/10.1007/s00021-012-0094-1)
• Asymptotic stability of boundary layers to the Euler-Poisson equations arising in plasma physics, SIAM J. Math. Anal., 44, (2012), 761–790
  S. Nishibata, M. Ohnawa, M. Suzuki
  (See online at https://doi.org/10.1137/110835657)
• Continuous limit of random walks and its application to approximation of nonlinear PDEs, RIMS Kôkyûroku, 1782, (2012), 122–134
  K. Soga
  
• Difference approximation to Aubry-Mather sets of the forced Burgers equation, Nonlinearity, 25, (2012), no. 9, 2401–2422
  T. Nishida, K. Soga
  (See online at https://doi.org/10.1088/0951-7715/25/9/2401)
• Eigenvalue problem for fully nonlinear second-order elliptic PDE on balls, Ann. Inst. H. Poincaré Anal. Non Linéaire, 29, (2012), no. 5, 783–812
  N. Ikoma, H. Ishii
  (See online at https://doi.org/10.1016/j.anihpc.2012.04.004)
• Fluid flows around floating bodies, I: The hydrostatic case, J. Math. Fluid Mech., 14, (2012), no. 4, 751–770
  J. Bemelmans, G. P. Galdi, M. Kyed
  (See online at https://doi.org/10.1007/s00021-011-0090-x)
• Global dynamics of difference equations for SIR epidemic models with a class of nonlinear incidence rates, Journal of Difference Equations and Applications, 18, (2012), 1163-1181
  Y. Enatsu, G. Izzo, Y. Muroya, Y. Nakata, A. Vecchio
  (See online at https://doi.org/10.1080/10236198.2011.555405)
• Global existence results for Oldroyd-B fluids in exterior domains, J. Differential Equations, 252, (2012), 2617–2629
  M. Hieber, Y. Naito, Y. Shibata
  (See online at https://doi.org/10.1016/j.jde.2011.09.001)
• Global existence results for Oldroyd-B fluids in exterior domains, J. Differential Equations, 252, (2012), no. 3, 2617–2629
  M. Hieber, Y. Naito, Y. Shibata
  (See online at https://doi.org/10.1016/j.jde.2011.09.001)
• Global stability for a discrete SIS epidemic model with immigration of infectives, Journal of Difference Equations and Applications, 18, (2012), 1913-1924
  Y. Enatsu, Y. Muroya, Y. Nakata
  (See online at https://doi.org/10.1080/10236198.2011.602973)
• Global well–posedness for the rotating Navier–Stokes–Boussinesq equations with stratification effects, Adv. Math. Sci. Appl., 22, (2012), no. 1, 61–90
  H. Koba, A. Mahalov, T. Yoneda
  
• Growth rate modeling and identification in the crystallization of polymers, Inverse Problems, 28, (2012), 13 pp.
  Y. Liu, M. Yamamoto, X. Xu
  (See online at https://doi.org/10.1088/0266-5611/28/9/095008)
• Influence of surface tension models on the hydrodynamics of wavy laminar falling films in Volume of Fluid-simulations, Int. J. Multiphase Flow., 43, (2012), 66–71
  C. Albert, D. Bothe, H. Raach
  (See online at https://doi.org/10.1016/j.ijmultiphaseflow.2012.02.011)
• Leray’s inequality for fluid flow in symmetric multi-connected two-dimensional domains, Tokyo J. Math., 35, (2012), 63–70
  R. Farwig, H. Morimoto
  (See online at https://doi.org/10.3836/tjm/1342701344)
• Leray’s inequality in general multi-connected domains in Rn, Math. Ann., 354, (2012), 137–145
  R. Farwig, H. Kozono, T. Yanagisawa
  (See online at https://doi.org/10.1007/s00208-011-0716-6)
• Lp-theory for a generalized nonlinear viscoelastic fluid model of differential type in various domains, Nonlinear Anal., 75, (2012), 5015–5026
  M. Geissert, D. G¨otz, M. Nesensohn
  (See online at https://doi.org/10.1016/j.na.2012.04.016)
• Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model, Nonlinear Analysis: Real World Applications, 13, (2012), 2120-2133
  Y. Enatsu, Y. Muroya, Y. Nakata
  (See online at https://doi.org/10.1016/j.nonrwa.2012.01.007)
• Maximal Lp-regularity for a 2D fluid-solid interaction problem, Spectral theory, mathematical system theory, evolution equations, differential and difference equations, Oper. Theory Adv. Appl., Birkhäuser, 221, (2012), 373–384
  K. Götze
  (See online at https://doi.org/10.1007/978-3-0348-0297-0_19)
• Motion of inertial particles in Gaussian fields driven by an infinite-dimensional fractional Brownian motion, Dyn. Syst., 27, (2012), 431–457
  G. Schöchtel
  (See online at https://doi.org/10.1080/14689367.2012.715143)
• On a generalization of the global attractivity for a periodically forced Pielou’s equation, J. of Difference Equations and Applications 18 (2012), 375-396
  K. Ishihara, Y. Nakata
  (See online at https://doi.org/10.1080/10236198.2010.503239)
• On radial solutions of inhomogeneous nonlinear scalar field equations, J. of Math. Anal. Appl., 386, (2012), 744–762
  N. Ikoma
  (See online at https://doi.org/10.1016/j.jmaa.2011.08.032)
• On the stationary Navier-Stokes flows around a rotating body, Manuscripta Math., 138, (2012), 315–345
  H. Heck, H. Kim, H. Kozono
  (See online at https://doi.org/10.1007/s00229-011-0494-1)
• On uniqueness of stationary solutions to the Navier-Stokes equations in exterior domains, Nonlinear Anal., 75, (2012), 3457–3464
  T. Nakatsuka
  (See online at https://doi.org/10.1016/j.na.2011.12.032)
• Propagation of the analyticity for the solution to the Euler equations with nondecaying initial velocity, RIMS Kôkyûroku Bessatsu, B33, (2012), 97–109
  O. Sawada, R. Takada
  
• The half-twisted splice operation on reduced knot projections, J. Knot Theory Ramifications, 21, (2012), no. 11, 10 pp.
  N. Ito, A. Shimizu
  (See online at https://doi.org/10.1142/S021821651250112X)
• The influence of frequency-limited and noise-contaminated sensing on reactive turbulence control schemes, J. Turbulence, 13, (2012)
  A. Stroh, B. Frohnapfel, Y. Hasegawa, N. Kasagi, C. Tropea
  (See online at https://doi.org/10.1080/14685248.2012.679343)
• The influence of frequency-limited and noise-contaminated sensing on reactive turbulence control schemes, J. Turbulence, 13, (2012)
  A. Stroh, B. Frohnapfel, Y. Hasegawa, N. Kasagi, C. Tropea
  (See online at https://doi.org/10.1080/14685248.2012.679343)
• Time periodic solutions to the Navier-Stokes equations in the rotational framework, J. Evol. Equ., 12, (2012), 985–1000
  T. Iwabuchi, R. Takada
  (See online at https://doi.org/10.1007/s00028-012-0165-z)
• Weak Neumann implies Stokes, J. Reine Angew. Math., 669, (2012), 75–100
  M. Geissert, H. Heck, M. Hieber, O. Sawada
  (See online at https://doi.org/10.1515/CRELLE.2011.150)
• Weak Neumann implies Stokes, J. Reine Angew. Math., 669, (2012), 75–100
  M. Geissert, H. Heck, M. Hieber, O. Sawada
  (See online at https://doi.org/10.1515/CRELLE.2011.150)
• A simple proof of Lq-estimates for the steady–state Oseen and Stokes equations in a rotating frame. Part I: Strong solutions, Proc. Amer. Math. Soc., 141, (2013), 573–583
  G. P. Galdi, M. Kyed
  (See online at https://doi.org/10.1090/S0002-9939-2012-11638-7)
• A simple proof of Lq-estimates for the steady–state Oseen and Stokes equations in a rotating frame. Part II: Weak solutions, Proc. Amer. Math. Soc., 141, (2013), 1313–1322
  G. P. Galdi, M. Kyed
  (See online at https://doi.org/10.1090/S0002-9939-2012-11640-5)
• Analytic rates of solutions to the Euler equations, Discrete Contin. Dyn. Syst. Ser. S, 6, (2013), no. 5, 1409–1415
  O. Sawada
  (See online at https://doi.org/10.3934/dcdss.2013.6.1409)
• Analyticity of the Stokes semigroup in spaces of bounded functions, Acta Math., 211, (2013), 1–46
  K. Abe, Y. Giga
  (See online at https://doi.org/10.1007/s11511-013-0098-6)
• Asymptotic profile of a linearized Navier-Stokes flow past a rotating body, Quart. Appl. Math., 71, (2013), no. 3, 489–500
  M. Kyed
  (See online at https://doi.org/10.1090/S0033-569X-2013-01288-7)
• Dispersive effect of the Coriolis force for the Navier-Stokes equations in the rotational framework, RIMS Kôkyûroku Bessatsu, B42, (2013), 137–152
  T. Iwabuchi, R. Takada
  
• Dynamical braces and dynamical Yang-Baxter map, Journal of Pure and Applied Algebra, 217, (2013), 195-206
  D. K. Matsumoto
  (See online at https://doi.org/10.1016/j.jpaa.2012.06.012)
• Existence of minimizers for some coupled nonlinear Schrödinger equations, Geometric properties for parabolic and elliptic PDE’s, Springer INdAM Ser., 2, Springer, Milan, (2013), 143–164
  N. Ikoma
  (See online at https://doi.org/10.1007/978-88-470-2841-8_10)
• Fluctuations in an Evolutional Model of Two-Dimensional Young Diagrams, Stochastic Process. Appl., 123, (2013), 1229–1275
  T. Funaki, M. Sasada, M. Sauer, B. Xie
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