Long time existence of the slightly compressible Navier-Stokes equations in bounded domains

Qiangchang Ju; Jianjun Xu

doi:10.3934/dcdsb.2023211

Article Contents

2024, Volume 29, Issue 7: 3022-3045. Doi: 10.3934/dcdsb.2023211

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Long time existence of the slightly compressible Navier-Stokes equations in bounded domains

Qiangchang Ju^{1, 2,} and
Jianjun Xu^{1, 3, ,}

1.
Institute of Applied Physics and Computational Mathematics, China
2.
National Key Laboratory of Computational Physics, China
3.
Graduate School of China Academy of Engineering Physics, China

^*Corresponding author: Jianjun Xu
^*Corresponding author: Jianjun Xu

Received: September 2023

Revised: December 2023

Early access: December 2023

Published: July 2024

The first author is supported by NSFC grants 12071044 and 12131007.

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Abstract

We are concerned with the long time existence of strong solutions to the initial boundary value problem with slip boundary conditions for the compressible Navier-Stokes equations in three-dimensional simply connected bounded domains. We verify that the barotropic Navier-Stokes equations admit a unique strong solution on the time interval where the solution to the incompressible Navier-Stokes equations exists and is reasonably smooth, when the Mach number is sufficiently small. Furthermore, we obtain the uniform convergence of strong solutions for the compressible system toward those for the corresponding incompressible system on that time interval.

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Mathematics Subject Classification: Primary: 35A01; Secondary: 76N06, 76N10.

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