Justification of the Hydrostatic Approximation of the Primitive Equations in Anisotropic Space L^∞_H L^q_x3(\Torus³)

2021/09/07 by Furukawa, Ken, Kashiwabara, Takahito
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.02879

Abstract

The primitive equations are fundamental models in geophysical fluid dynamics and derived from the scaled Navier-Stokes equations. In the primitive equations, the evolution equation to the vertical velocity is replaced by the so-called hydrostatic approximation. In this paper, we give a justification of the hydrostatic approximation by the scaled Navier-Stoke equations in anisotropic spaces L^∞_H L^q_x3 (\Torus³) for q ≥ 1.

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