Hydrostatic approximation of the 2D primitive equations in a thin strip

Nacer Aarach; Van-Sang Ngo

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arXiv · 2006.16025

Hydrostatic approximation of the 2D primitive equations in a thin strip

Nacer Aarach·Van-Sang Ngo

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Abstract

We prove the global wellposedness of the 2D non-rotating primitive equations with no-slip boundary conditions in a thin strip of width $\eps$ for small data which are analytic in the tangential direction. We also prove that the hydrostatic limit (when $\eps \to 0$) is a couple of a Prandtl-like system for the velocity with a transport-diffusion equation for the temperature.

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Nacer Aarach, Van-Sang Ngo. 2020-06-29. Hydrostatic approximation of the 2D primitive equations in a thin strip. https://arxiv.org/abs/2006.16025

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