Shock waves in conservation laws with physical viscosity
Author(s)
Bibliographic Information
Shock waves in conservation laws with physical viscosity
（Memoirs of the American Mathematical Society, no. 1105）
American Mathematical Society, 2015, c2014
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Note
Volume 234, number 1105 (fifth of 5 numbers), March 2015"
Includes bibliographical references (p. 167-168)
Description and Table of Contents
Description
The authors study the perturbation of a shock wave in conservation laws with physical viscosity. They obtain the detailed pointwise estimates of the solutions. In particular, they show that the solution converges to a translated shock profile. The strength of the perturbation and that of the shock are assumed to be small but independent. The authors' assumptions on the viscosity matrix are general so that their results apply to the Navier-Stokes equations for the compressible fluid and the full system of magnetohydrodynamics, including the cases of multiple eigenvalues in the transversal fields, as long as the shock is classical. The authors' analysis depends on accurate construction of an approximate Green's function. The form of the ansatz for the perturbation is carefully constructed and is sufficiently tight so that the author can close the nonlinear term through Duhamel's principle.
Table of Contents
Introduction
Preliminaries
Green's functions for systems with constant coefficients
Green's function for systems linearized along shock profiles
Estimates on Green's function
Estimates on crossing of initial layer
Estimates on truncation error
Energy type estimates
Wave interaction
Stability analysis
Application to magnetohydrodynamics
Bibliography
by "Nielsen BookData"