International Workshop on PDEs in Fluid Dynamics and Related Models, Shanghai Jiao Tong University, Nov.27-30, 2014.
http://math.sjtu.edu.cn/conference/FDRMPDE/speakers.html
In this talk, I will show a priori estimates for the three-dimensional compressible Euler equations with moving physical vacuum boundary, the $\gamma$-gas law equation of state for $\gamma=2$ and the general initial density $\rho_0 \in H^5$. I derive a mixed space-time interpolation inequality which play a vital role in the energy estimates and obtain some extra estimates for the space-time derivatives of the velocity in $L^3$, which is different from the known results.