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.
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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. 585–638DOI 10.4171/JEMS/1018