Shock formation in the compressible Euler equations and related systems
Analysis of PDEs
2012-05-23 v1
Abstract
We prove shock formation results for the compressible Euler equations and related systems of conservation laws in one space dimension, or three dimensions with spherical symmetry. We establish an bound for solutions of the one-D Euler equations, and use this to improve recent shock formation results of the authors. We prove analogous shock formation results for one-D MHD with orthogonal magnetic field, and for compressible flow in a variable area duct, which has as a special case spherically symmetric three dimensional flow on the exterior of a ball
Cite
@article{arxiv.1205.4995,
title = {Shock formation in the compressible Euler equations and related systems},
author = {Geng Chen and Robin Young and Qingtian Zhang},
journal= {arXiv preprint arXiv:1205.4995},
year = {2012}
}