Gevrey stability of hydrostatic approximate for the Navier-Stokes equations in a thin domain

Abstract

In this paper, we justify the limit from the Navier-Stokes system in a thin domain to the hydrostatic Navier-Stokes/Prandtl system for the convex initial data with Gevrey 9/8 regualrity in $x$.

31 pages

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• Optimal Gevrey stability of hydrostatic approximation for the Navier-Stokes equations in a thin domain