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The initial–boundary-value problem for real viscous heat-conducting flow with shear viscosity

Published online by Cambridge University Press:  12 July 2007

Dehua Wang
Dehua Wang
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA (dwang@math.pitt.edu)
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Abstract

An initial–boundary-value problem for the nonlinear equations of real compressible viscous heat-conducting flow with general large initial data is investigated. The main point is to study the real flow for which the pressure and internal energy have nonlinear dependence on temperature, unlike the linear dependence for ideal flow, and the viscosity coefficients and heat conductivity are also functions of density and/or temperature. The shear viscosity is also presented. The existence, uniqueness and regularity of global solutions are established with large initial data in H1. It is shown that there is no shock wave, vacuum, mass concentration, or heat concentration (hot spots) developed in a finite time, although the solutions have large oscillations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 4 , August 2003 , pp. 969 - 986
Copyright
Copyright © Royal Society of Edinburgh 2003

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