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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
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