Justification of the Hydrostatic Approximation of the Primitive Equations in Anisotropic Space $L^\infty_H L^q_{x_3}(\Torus^3)$

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 $L^\infty_H L^q_{x_3} (\Torus^3)$ for $q\ge 1$.

References in corpus (4)

• Global Strong Well-posedness of the Three Dimensional Primitive equations in $L^p$-spaces
• Analyticity of solutions to the primitive equations
• Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier-Stokes equations
• The Hydrostatic Stokes Semigroup and Well-Posedness of the Primitive Equations on Spaces of Bounded Functions