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Choi, Kyudong
Fluids Analysis Lab
Research Interests
  • fluid equations, mathematical biology, conservation laws,

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Short-time stability of scalar viscous shocks in the inviscid limit by the relative entropy method

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Title
Short-time stability of scalar viscous shocks in the inviscid limit by the relative entropy method
Author
Choi, KyudongAlexis Vasseur
Issue Date
2015-04
Publisher
SIAM PUBLICATIONS
Citation
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, v.47, no.2, pp.1405 - 1418
Abstract
We consider inviscid limits to shocks for viscous scalar conservation laws in one space dimension, with strict convex fluxes. We show that we can obtain sharp estimates in L-2 for a class of large perturbations and for any bounded time interval. Those perturbations can be chosen big enough to destroy the viscous layer. This shows that the fast convergence to the shock does not depend on the fine structure of the viscous layers. This is the first application of the relative entropy method developed by N. Leger [Arch. Ration. Mech. Anal., 199 (2011), pp. 761-778] and N. Leger and A. Vasseur [Arch. Ration. Mech. Anal., 201 (2011), pp. 271-302] to the study of an inviscid limit to a shock.
URI
https://scholarworks.unist.ac.kr/handle/201301/13055
URL
http://epubs.siam.org/doi/10.1137/140961523
DOI
10.1137/140961523
ISSN
0036-1410
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