CYBER DEAL: 50% off all Springer eBooks | Get this offer!

Applied Mathematical Sciences

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

Authors: Majda, A.

Free Preview

eBook $109.00 price for USA in USD • ISBN 978-1-4612-1116-7 • Digitally watermarked, DRM-free • Included format: PDF • ebooks can be used on all reading devices • Immediate eBook download after purchase Softcover$139.99
price for USA in USD

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.

• Introduction

Pages 1-29

Majda, A.

• Smooth Solutions and the Equations of Incompressible Fluid Flow

Pages 30-80

Majda, A.

• The Formation of Shock Waves in Smooth Solutions

Pages 81-110

Majda, A.

• The Existence and Stability of Shock Fronts in Several Space Variables

Pages 111-156

Majda, A.

eBook $109.00 price for USA in USD • ISBN 978-1-4612-1116-7 • Digitally watermarked, DRM-free • Included format: PDF • ebooks can be used on all reading devices • Immediate eBook download after purchase Softcover$139.99
price for USA in USD

## Bibliographic Information

Bibliographic Information
Book Title
Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables
Authors
Series Title
Applied Mathematical Sciences
Series Volume
53
1984
Publisher
Springer-Verlag New York