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

  • A. Majda

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

Table of contents

  1. Front Matter
    Pages i-viii
  2. A. Majda
    Pages 1-29
  3. Back Matter
    Pages 157-159

About this book

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

  • A. Majda
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

Bibliographic information

  • 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 Springer Book Archive
  • Print ISBN 978-0-387-96037-1
  • Online ISBN 978-1-4612-1116-7
  • Series Print ISSN 0066-5452
  • About this book