Memoirs of the American Mathematical Society
2014; 168 pp; Softcover
MSC: Primary 35; Secondary 76

Electronic ISBN: 978-1-4704-2032-1
Product Code: MEMO/234/1105.E
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Shock Waves in Conservation Laws with Physical Viscosity

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Tai-Ping Liu; Yanni Zeng

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.

Shock Waves in Conservation Laws with Physical Viscosity

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Title (HTML): Shock Waves in Conservation Laws with Physical Viscosity

Author(s) (Product display): Tai-Ping Liu; Yanni Zeng

Affiliation(s) (HTML): Institute of Mathematics, Academia Sinica, Taipei, Taiwan and Stanford University, Stanford, CA; University of Alabama at Birmingham, Birmingham, AL

Abstract:

Book Series Name: Memoirs of the American Mathematical Society

Publication Month and Year: 2015-02-06

Page Count: 168

Cover Type: Softcover

Print ISBN-13: 978-1-4704-1016-2

Online ISBN 13: 978-1-4704-2032-1

Print ISSN: 0065-9266

Online ISSN: 0065-9266

Primary MSC: 35

Secondary MSC: 76

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Cover
- Cover
Title page
- Title page
Chapter 1. Introduction
- Chapter 1. Introduction
Chapter 2. Preliminaries
- Chapter 2. Preliminaries

Shock Waves in Conservation Laws with Physical Viscosity

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Shock Waves in Conservation Laws with Physical Viscosity

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Title page

Chapter 1. Introduction

Chapter 2. Preliminaries