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Time-asymptotic stability of composite waves of viscous shock and rarefaction for barotropic Navier-Stokes equations by Moon-Jin Kang; Alexis F. Vasseur; Yi Wang is a Mathematics article available to read on EtoBox.

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We prove the time-asymptotic stability of composite waves consisting of the superposition of a viscous shock and a rarefaction for the one-dimensional compressible barotropic Navier-Stokes equations. Our result solves a long-standing problem first mentioned in 1986 by Matsumura and Nishihara in [28]. The same authors introduced it officially as an open problem in 1992 in [29] and it was again described as very challenging open problem in 2018 in the survey paper [26]. The main difficulty is due to the incompatibility of the standard anti-derivative method, used to study the stability of viscous shocks, and the energy method used for the stability of rarefactions. Instead of the anti-derivative method, our proof uses the a-contraction with shifts theory recently developed by two of the authors. This method is energy based, and can seamlessly handle the superposition of waves of different kinds.

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Author

Moon-Jin Kang; Alexis F. Vasseur; Yi Wang

Publisher

Elsevier BV

Published

2023

Language

EN

Field

Mathematics (Physical Sciences)