# Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables

Book

Part of the Applied Mathematical Sciences book series (AMS, volume 53)

1. Front Matter
Pages i-viii
2. A. Majda
Pages 1-29
3. A. Majda
Pages 30-80
4. A. Majda
Pages 81-110
5. A. Majda
Pages 111-156
6. Back Matter
Pages 157-159

### Introduction

Conservation laws arise from the modeling of physical processes through the following three steps: 1) The appropriate physical balance laws are derived for m-phy- t cal quantities, ul""'~ with u = (ul' ... ,u ) and u(x,t) defined m for x = (xl""'~) E RN (N = 1,2, or 3), t > 0 and with the values m u(x,t) lying in an open subset, G, of R , the state space. The state space G arises because physical quantities such as the density or total energy should always be positive; thus the values of u are often con­ strained to an open set G. 2) The flux functions appearing in these balance laws are idealized through prescribed nonlinear functions, F.(u), mapping G into J j = 1, ..• ,N while source terms are defined by S(u,x,t) with S a given smooth function of these arguments with values in Rm. In parti- lar, the detailed microscopic effects of diffusion and dissipation are ignored. 3) A generalized version of the principle of virtual work is applied (see Antman [1]). The formal result of applying the three steps (1)-(3) is that the m physical quantities u define a weak solution of an m x m system of conservation laws, o I + N(Wt'u + r W ·F.(u) + W·S(u,x,t))dxdt (1.1) R xR j=l Xj J for all W E C~(RN x R+), W(x,t) E Rm.

### Keywords

Erhaltungssatz Gasdynamik Kompressible Strömung Stosswelle Systems flow

#### Authors and affiliations

1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

### Bibliographic information

• Book Title Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables
• Authors A. Majda
• Series Title Applied Mathematical Sciences
• DOI https://doi.org/10.1007/978-1-4612-1116-7
• Copyright Information Springer-Verlag New York Inc. 1984
• Publisher Name Springer, New York, NY
• eBook Packages
• Softcover ISBN 978-0-387-96037-1
• eBook ISBN 978-1-4612-1116-7
• Series ISSN 0066-5452
• Edition Number 1
• Number of Pages , 172
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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