Open Access
September 2009 On the formation of shocks to the compressible Euler equations
Dongho Chae, Seung-Yeal Ha
Commun. Math. Sci. 7(3): 627-634 (September 2009).


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.


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Dongho Chae. Seung-Yeal Ha. "On the formation of shocks to the compressible Euler equations." Commun. Math. Sci. 7 (3) 627 - 634, September 2009.


Published: September 2009
First available in Project Euclid: 26 October 2009

zbMATH: 1183.35225
MathSciNet: MR2569026

Primary: 35B30 , 35Q35

Keywords: Blow-up , compressible Euler equations , particle trajectory , shock wave , vacuum boundary

Rights: Copyright © 2009 International Press of Boston

Vol.7 • No. 3 • September 2009
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