Communications in Mathematical Sciences

On the formation of shocks to the compressible Euler equations

Dongho Chae and Seung-Yeal Ha

Full-text: Open access


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 information

Commun. Math. Sci., Volume 7, Number 3 (2009), 627-634.

First available in Project Euclid: 26 October 2009

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q35: PDEs in connection with fluid mechanics 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]

Compressible Euler equations blow-up shock wave particle trajectory vacuum boundary


Chae, Dongho; Ha, Seung-Yeal. On the formation of shocks to the compressible Euler equations. Commun. Math. Sci. 7 (2009), no. 3, 627--634.

Export citation