Contraction property for large perturbations of shocks of the barotropic Navier–Stokes system
Moon-Jin Kang
Korea Advanced Institute of Science and Technology (KAIST), Daejeon, KoreaAlexis F. Vasseur
The University of Texas at Austin, USA
![Contraction property for large perturbations of shocks of the barotropic Navier–Stokes system cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jems-volume-23-issue-2.png&w=3840&q=90)
Abstract
This paper is dedicated to the construction of a pseudo-norm for which small shockprofiles of the barotropic Navier–Stokes equations have a contraction property. This contraction property holds in the class of any large solutions to the barotropic Navier–Stokes equations. It implies a stability condition which is independent of the strength of the viscosity. The proof is based on the relative entropy method, and is related to the notion of -contraction first introduced by the authors in the hyperbolic case.
Cite this article
Moon-Jin Kang, Alexis F. Vasseur, Contraction property for large perturbations of shocks of the barotropic Navier–Stokes system. J. Eur. Math. Soc. 23 (2021), no. 2, pp. 585–638
DOI 10.4171/JEMS/1018