**Memoirs of the American Mathematical Society**

2014;
168 pp;
Softcover

MSC: Primary 35;
Secondary 76

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

Product Code: MEMO/234/1105

List Price: $89.00

Individual Member Price: $53.40

**Electronic ISBN: 978-1-4704-2032-1
Product Code: MEMO/234/1105.E**

List Price: $89.00

Individual Member Price: $53.40

# 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.

#### Table of Contents

# Table of Contents

## Shock Waves in Conservation Laws with Physical Viscosity

- Cover Cover11 free
- Title page i2 free
- Chapter 1. Introduction 18 free
- Chapter 2. Preliminaries 1522 free
- Chapter 3. Green’s functions for Systems with Constant Coefficients 2330
- Chapter 4. Green’s Function for Systems Linearized Along Shock Profiles 3542
- Chapter 5. Estimates on Green’s Function 4552
- Chapter 6. Estimates on Crossing of Initial Layer 6370
- Chapter 7. Estimates on Truncation Error 7178
- Chapter 8. Energy Type Estimates 101108
- Chapter 9. Wave Interaction 111118
- Chapter 10. Stability Analysis 123130
- Chapter 11. Application to Magnetohydrodynamics 163170
- References 167174
- Back Cover Back Cover1180