Preprint 2003-053

Spatially Periodic Solutions in Relativistic Isentropic Gas Dynamics

Hermano Frid and Mikhail Perepelitsa

Abstract: We consider the initial value problem, with periodic initial data, for the Euler equations in relativistic isentropic gas dynamics, for ideal polytropic gases which obey a constitutive equation, relating pressure $p$ and density $\rho$, $p=\k^2\rho^\g$, with $\g\ge1$, $0<\k<c$, where $c$ is the speed of light. Global existence of periodic entropy solutions for initial data sufficiently close to a constant state follows from a celebrated result of Glimm and Lax (1970). We prove that given any periodic initial data of locally bounded total variation, satisfying the physical restrictions $0<\inf_{x\in\R}\rho_0(x)<\sup_{x\in\R}\rho_0(x)<+\infty$, $\|v_0\|_\infty<c$, where $v$ is the gas velocity, there exists a globally defined spatially periodic entropy solution for the Cauchy problem, if $1\le \g<\g_0$, for some $\g_0>1$, depending on the initial bounds. The solution decays in $L_{loc}^1$ to its mean value as $t\to \infty$.



Paper:
Available as PDF (392 Kbytes).
Author(s):
Hermano Frid, <hermano@impa.br>
Mikhail Perepelitsa, <mikhailp@math.northwestern.edu>
Publishing information:
Comments:
Submitted by:
<hermano@impa.br> August 22 2003.


[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 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 <conservation@math.ntnu.no>
Last modified: Mon Aug 25 11:03:48 MEST 2003