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

Abstract

In this paper, we study the hydrostatic approximation for the Navier-Stokes system in a thin domain. When the convex initial data with Gevrey regularity of optimal index 3/2 in x variable and Sobolev regularity in y variable, we justify the limit from the anisotropic Navier-Stokes system to the hydrostatic Navier-Stokes/Prandtl system. Due to our method in the paper is independent of ε, by the same argument, we also get the hydrostatic Navier-Stokes/Prandtl system is well-posedness in the optimal Gevrey space. Our results improve the Gevrey index in [14, 34] whose Gevrey index is 9/8 .

arXiv comment39 pages

References in corpus (6)

• On the ill-posedness of the Prandtl equation
• Gevrey Stability of Prandtl Expansions for 2D Navier-Stokes
• Vanishing Viscous Limits for 3D Navier-Stokes Equations with A Navier-Slip Boundary Condition
• The inviscid limit of Navier-Stokes for analytic data on the half-space
• Gevrey stability of hydrostatic approximate for the Navier-Stokes equations in a thin domain
• Optimal Prandtl expansion around concave boundary layer