Project Details
Projekt
Existence, uniqueness and regularity of geophysical flows
Applicant
Dr. Tim Binz
Subject Area
Mathematics
Term
since 2024
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 538212014
The subject of this project is the analysis of different geophysical flows: 1. primitive equations. These equations describe the dynamic of ocean and atmosphere. They have applications in weather forecast. In this subproject I would like to study the behaviour of weak solutions of the primitive equations. In particular, I would like to investigate the uniqueness and the question of conservation of energy of such solutions. 2. surface quasi-geostrophic equations (SQG). These equations describe the temperature in rapidly rotating systems. The inviscid SQG has structural similarities with the three dimensional Euler equations, whereas the critical, dissipative SQG has structural similarities with the three dimensional Navier-Stokes equations. Therefore SQG are interesting toy problems to study phenomena in fluid dynamics. In this subproject I would like to generalize existing uniqueness, existence and regularity results to (curve, two dimensional) surfaces (and more general to two dimensional manifolds with boundary). 3. The interaction between a fluid and a poro-viscoelastic material. We consider a rigid body, consisting of a poro-viscoelastic material, which is enclosed by a fluid. Poro-viscoelastic materials are materials, which show partially porous, partially viscous and partially elastic effects. They are modelled by the Biot equation, whereas the dynamic of the fluid is discribed by the three dimensional Navier-Stokes equations. The interaction at the interface can be discribed by coupled boundary conditions: the so called Beaver-Joseph-Saffman conditions. The aim of this subproject is the study of global existence and uniqueness of strong solutions for such systems for small initial data.
DFG Programme
WBP Fellowship
International Connection
USA
