Invited talk,第十五届非线性偏微分方程暑期讲习班暨学术会议, 2017.08.01-03,西北大学,西安。
摘要: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.