JUSTIFICATION OF THE HYDROSTATIC APPROXIMATION OF THE PRIMITIVE EQUATIONS IN ANISOTROPIC SPACE L∞HLqx3 (T3)

Ken Furukawa; Takahito Kashiwabara

JUSTIFICATION OF THE HYDROSTATIC APPROXIMATION OF THE PRIMITIVE EQUATIONS IN ANISOTROPIC SPACE L^∞H^Lqx₃ (T³)

Ken Furukawa, Takahito Kashiwabara

Program of Mathematics and Informatics

Research output: Contribution to journal › Article › peer-review

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-Stokes equations in anisotropic spaces L^∞H^Lqx₃ (T³) for q ≥ 1.

Original language	English
Pages (from-to)	45-71
Number of pages	27
Journal	Advances in Mathematical Sciences and Applications
Volume	31
Issue number	1
State	Published - 2022

Keywords

anisotropic function spaces
hydrostatic approximation
the Navier-Stokes equations
the primitive equations

ASJC Scopus subject areas

Analysis
Applied Mathematics
Modeling and Simulation
Numerical Analysis

Cite this

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