We present an explicit upper-bound for the life-span of C3-smooth solutions
to the multi-dimensional compressible Euler equations with a certain class
of initial data containing compression vacuum states. We also show that the
divergence of a fluid velocity will blow up along the particle trajectories
issued from the compression vacuum states, which represent a shock formation
at the vacuum states.
@article{1256562816,
author = {Chae, Dongho and Ha, Seung-Yeal},
title = {On the formation of shocks to the compressible Euler equations},
journal = {Commun. Math. Sci.},
volume = {7},
number = {1},
year = {2009},
pages = { 627-634},
language = {en},
url = {http://dml.mathdoc.fr/item/1256562816}
}
Chae, Dongho; Ha, Seung-Yeal. On the formation of shocks to the compressible Euler equations. Commun. Math. Sci., Tome 7 (2009) no. 1, pp. 627-634. http://gdmltest.u-ga.fr/item/1256562816/