应304am永利集团官网耿俊教授和王跃循教授邀请，清华大学数学科学系何凌冰教授将于2022年9月30日上午在线举办学术报告。

报告题目:Global strong solutions of 3D Compressible Navier-Stokes equations with short pulse type initial data

时 间：9月30日（星期五）10：00

腾讯会议ID：871 175 104

报告摘要：Short pulse initial datum is referred to the one supported in the ball of radius $\delta$ and with amplitude $\delta^{\f12}$ which looks like a pulse. It was first introduced by Christodoulou to prove the formation of black holes for Einstein equations and also to catch the shock formation for compressible Euler equations. The aim of this talk is to consider the same type initial data, which allow the density of the fluid to have large amplitude $\delta^{-\frac{\alpha}{\gamma}}$ with $\delta\in(0,1]$ for the compressible Navier-Stokes equations. We prove the global well-posedness and show that the initial bump region of the density with large amplitude will disappear within a very short time. As a consequence, we obtain the global dynamic behavior of the solutions and the boundedness of $\|\na\vv u\|_{L^1([0,\infty);L^\infty)}$. The key ingredients of the proof lie in the new observations for the effective viscous flux and new decay estimates for the density via the Lagrangian coordinate.

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何凌冰教授简介

何凌冰，清华大学数学科学系教授、博士生导师。何凌冰教授主要从事流体力学和动理学偏微分方程的理论研究，在相关课题上取得了重要研究成果，目前已在“Ann. Sci.Éc. Norm. Supér.”、“Ann. PDE”、“Comm. Math. Phys.”、“Arch. Ration. Mech. Anal.”、“Math. Ann.”等国际重要学术期刊上发表论文多篇。

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萃英学院

2022年9月27日