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

Wang, Ya-Guang; Zhu, Shi-Yong

doi:10.1090/qam/1488

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
MathSciNet review: 3805039
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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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