Communications in Mathematical Sciences
Volume 7 (2009)
On the formation of shocks to the compressible Euler equations
Pages: 627 – 634
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.
Compressible Euler equations; blow-up; shock wave; particle trajectory; vacuum boundary
2010 Mathematics Subject Classification