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arXiv · 2106.06077

Uniform regularity for the compressible Navier-Stokes system with low Mach number in bounded domains

Nader Masmoudi·Frédéric Rousset·Changzhen Sun
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Abstract

We establish uniform with respect to the Mach number regularity estimates for the isentropic compressible Navier-Stokes system in smooth domains with Navier-slip condition on the boundary in the general case of ill-prepared initial data. To match the boundary layer effects due to the fast oscillations and the ill-prepared initial data assumption, we prove uniform estimates in an anisotropic functional framework with only one normal derivative close to the boundary. This allows to prove the local existence of a strong solution on a time interval independent of the Mach number and to justify the incompressible limit through a simple compactness argument.

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Nader Masmoudi, Frédéric Rousset, Changzhen Sun. 2021-06-10. Uniform regularity for the compressible Navier-Stokes system with low Mach number in bounded domains. https://arxiv.org/abs/2106.06077

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