Preprint 1999-033

Global Weak Solutions to the Navier-Stokes Equations for a 1D Viscous Polytropic Ideal Gas

S. Jiang and P. Zhang

Abstract: We prove the existence of global weak solutions to the Navier-Stokes equations for a one-dimensional viscous polytropic ideal gas. We require only that the initial density is in $L^\infty\cap L^2_{loc}$ with positive infimum, the initial velocity is in $L^2$ and the initial temperature is in a larger space than $L^2$ with positive infimum. The initial density and the initial velocity may have differing constant states at $x=\pm\infty$. In particular, piesewise constant data with arbitrary large jump discontinuities are included. Our results show that neither vacuum states nor concentration states can form and the temperature remains positive in finite time.

Available as PostScript.
S. Jiang, <>
P. Zhang, <>
Publishing information:
Submitted by:
<> October 10 1999.

[ 1996 | 1997 | 1998 | 1999 | All Preprints | Preprint Server Homepage ]
© The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

Conservation Laws Preprint Server <>
Last modified: Wed Oct 13 10:14:33 1999