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

**中科院数学与系统科学研究院**

**数学研究所**

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**偏微分方程研讨班**

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#### 题目/Title: Free-boundary compressible Euler equations and the incompressible limit

**Speaker：**Dr. Chenyun Luo (Vanderbilt University, USA)

**Time:** 16:00-17:00, Jan. 4, 2019 (Fri)

**Place:** Rm. 915, Siyuan Building

**Abstract:** We present a new type of energy estimates for the compressible Euler equations with free boundary, with a boundary part and an interior part. These can be thought of as a generalization of the energies in Christodoulou and Lindblad to the compressible case and do not require the fluid to be irrotational. Furthermore, the estimate is uniform as the sound speed of the liquid goes to infinity, which allows us to show the convergence of the solution for compressible Euler equations to that of the incompressible equations in $C^2$. In particular, we can approximate the solution of a compressible gravity water wave by that of an incompressible water wave, whose global in time solution is known to exist. This work opens up a new approach to proving long time existence also for compressible water waves with small data, as conjectured by Hans Lindblad.

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