郝成春的个人主页 | Chengchun HAO's Homepage

研究员、博士生导师，中国科学院数学与系统科学研究院 数学研究所 | Professor, Institute of Mathematics, AMSS, CAS

#### On the free boundary problem of compressible Euler equations in physical vacuum with general initial densities

Invited talk, IAPCM, June 3th, 2017.

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.

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