Lower bound of density for Lipschitz continuous solutions in the isentropic gas dynamics
Abstract
For the Euler equations of isentropic gas dynamics in one space dimension, also knowns as psystem in Lagrangian coordinate, it is known that the density can be arbitrarily close to zero as time goes to infinity, even when initial density is uniformly away from zero. In this paper, for uniform positive initial density, we prove the density in any Lipschitz continuous solutions for Cauchy problem has a sharp positive lower bound in the order of O(1/(1+t)), which is identified by explicit examples in [9](Courant and Friedrichs, Supersonic Flow and Shock Waves, 1948.).
 Publication:

arXiv eprints
 Pub Date:
 October 2014
 arXiv:
 arXiv:1410.3182
 Bibcode:
 2014arXiv1410.3182C
 Keywords:

 Mathematics  Analysis of PDEs