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Shock waves in conservation laws with physical viscosity
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eBook
Shock waves in conservation laws with physical viscosity
2015
Overview
We study the perturbation of a shock wave in conservation laws with physical viscosity. We obtain the detailed pointwise estimates of
the solutions. In particular, we 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. Our assumptions on the viscosity matrix are general so that our 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. Our 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 we
can close the nonlinear term through the Duhamel’s principle.
Publisher
American Mathematical Society
Subject
ISBN
9781470410162, 1470410168
