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Rigorous Justification of the Hydrostatic Approximation from the Navier-Stokes Equations to the Primitive Equations

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TURW05 - Advances in geophysical and astrophysical turbulence

The hydrostatic approximation, which can be formally derived as small aspect ratio (the ratio of the vertical scale to the horizontal scale) limit, is a fundamental assumption in the geophysics and in particular for the large scale ocean and atmospheric dynamics. In this talk we provide a justification of the hydrostatic approximation in the frameworks of both strong solutions and $z$-weak solutions and at the same time get the convergence rate. Both the isotropic case (that is with viscosities in all directions) and anisotropic cases (that is with viscosities in the horizontal directions only) will be considered.  This talk is based on joint works with E. S. Titi and G. Yuan. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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