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Global existence for the primitive equations with small anisotropic viscosity. (English) Zbl 1228.35175

The paper deals with the anisotropic primitive equations with zero vertical viscosity and zero vertical thermal diffusivity. In addition, the horizontal viscosity and thermal diffusivity tend to zero when the rotation tends to infinity. Under sufficiently fast rotation the convergence to the quasi-geostrophic system and the global existence of a unique strong solution are proved.

MSC:

35Q35 PDEs in connection with fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76U05 General theory of rotating fluids
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References:

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