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Shock waves in conservation laws with physical viscosity /
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...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2015.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1105. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | 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. |
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| Notas: | "Volume 234, number 1105 (fifth of 5 numbers), March 2015." |
| Descripción Física: | 1 online resource (v, 168 pages) : illustrations |
| Bibliografía: | Includes bibliographical references (pages 167-168). |
| ISBN: | 9781470420321 1470420325 |
| ISSN: | 0065-9266 ; |