Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the inviscid limit for the compressible Navier-Stokes system with no-slip boundary condition

Authors: Ya-Guang Wang and Shi-Yong Zhu
Journal: Quart. Appl. Math. 76 (2018), 499-514
MSC (2010): Primary 35Q30, 76N20
DOI: https://doi.org/10.1090/qam/1488
Published electronically: October 31, 2017
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Abstract: The proposal of this paper is to study the convergence of the compressible Navier-Stokes equations with no-slip boundary condition to the corresponding problem of the Euler equations in a smooth bounded domain $ \Omega \subseteq \mathbb{R}^{3}$. Motivated by Wang's work (2001), we obtain a sufficient condition for the convergence to take place in the energy space $ L^{2}(\Omega )$ uniformly in time, by using Kato's idea (1984) of constructing an artificial boundary layer. This improves the result of Sueur in the sense that this sufficient condition contains the tangential or the normal component of velocity only.

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Ya-Guang Wang
Affiliation: Department of Mathematics, MOE-LSC and SHL-MAC, Shanghai Jiao Tong University, Shanghai, People’s Republic of China
Email: ygwang@sjtu.edu.cn

Shi-Yong Zhu
Affiliation: Department of Mathematics, Shanghai Jiao Tong University, Shanghai, People’s Republic of China
Email: shiyong_zhu@sjtu.edu.cn

DOI: https://doi.org/10.1090/qam/1488
Keywords: Inviscid limit, compressible Navier-Stokes system, no-slip condition
Received by editor(s): March 21, 2017
Received by editor(s) in revised form: August 22, 2017
Published electronically: October 31, 2017
Article copyright: © Copyright 2017 Brown University

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