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OPTIMAL GEVREY STABILITY OF HYDROSTATIC APPROXIMATION FOR THE NAVIER-STOKES EQUATIONS IN A THIN DOMAIN

Part of: Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  06 September 2023

Chao Wang  and
Yuxi Wang Open the ORCID record for Yuxi Wang [Opens in a new window]
Chao Wang
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, China ([email protected])
Yuxi Wang*
Affiliation:
School of Mathematics, Sichuan University, Chengdu 610064, China
*
[email protected]
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Abstract

In this paper, we study the hydrostatic approximation for the Navier-Stokes system in a thin domain. When we have convex initial data with Gevrey regularity of optimal index $\frac {3}{2}$ in the x variable and Sobolev regularity in the 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 being independent of $\varepsilon $, by the same argument, we also obtain the well-posedness of the hydrostatic Navier-Stokes/Prandtl system in the optimal Gevrey space. Our results improve upon the Gevrey index of $\frac {9}{8}$ found in [15, 35].

Keywords

Navier-Stokes equationshydrostatic approximationthin domain

MSC classification

Primary: 35Q30: Navier-Stokes equations
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 23 , Issue 4 , July 2024 , pp. 1521 - 1566
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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