Shock formation in the compressible Euler equations and related systems

Geng Chen, Robin Young, Qingtian Zhang

Published 2012-05-22Version 1

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 $L^\infty$ bound for $C^1$ 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