Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model. (English) Zbl 1037.76012
Summary: We consider a two-dimensional viscous shallow water model with friction term. Existence of global weak solutions is obtained and convergence to the strong solution of the viscous quasi-geostrophic equation with free surface term is proven in the well prepared case. The ill prepared data case is also discussed.
MSC:
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
| 35Q35 | PDEs in connection with fluid mechanics |
| 86A05 | Hydrology, hydrography, oceanography |
| 35D05 | Existence of generalized solutions of PDE (MSC2000) |
| 76U05 | General theory of rotating fluids |
