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arXiv · 2206.03873

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

Chao Wang·Yuxi Wang
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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 {\epsilon}, 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 .

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Chao Wang, Yuxi Wang. 2022-06-08. Optimal Gevrey stability of hydrostatic approximation for the Navier-Stokes equations in a thin domain. https://doi.org/10.1017/s1474748023000282

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