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

2012/10/29 by Kyudong Choi, Alexis Vasseur, Choi, Kyudong +1
Mathematics · Physics and Astronomy · Engineering · #Navier-Stokes equation solutions #Cosmology and Gravitation Theories #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.1210.7853

Abstract

We consider inviscid limits to shocks for viscous scalar conservation laws in\none space dimension, with strict convex fluxes. We show that we can obtain\nsharp estimates in L², for a class of large perturbations and for any\nbounded time interval. Those perturbations can be chosen big enough to destroy\nthe viscous layer. This shows that the fast convergence to the shock does not\ndepend on the fine structure of the viscous layers. This is the first\napplication of the relative entropy method developed in [22], [23] to the study\nof an inviscid limit to a shock.\n

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