Communications in Mathematical Sciences
- Commun. Math. Sci.
- Volume 7, Number 3 (2009), 627-634.
On the formation of shocks to the compressible Euler equations
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.
Commun. Math. Sci., Volume 7, Number 3 (2009), 627-634.
First available in Project Euclid: 26 October 2009
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Chae, Dongho; Ha, Seung-Yeal. On the formation of shocks to the compressible Euler equations. Commun. Math. Sci. 7 (2009), no. 3, 627--634. https://projecteuclid.org/euclid.cms/1256562816