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线上学术报告-----何凌冰教授（清华大学）

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

报告人：何凌冰教授（清华大学）Lingbing He (Tsinghua University)

报告时间：2022年10月7日星期五下午15：00—16：00

腾讯会议号：693 720 817
密码：1007

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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专家简介：

何凌冰，清华大学数学科学系教授、博士生导师。何凌冰教授主要研究方向为Boltzmann方程及Landau方程解的正则性传播和渐进性行为，已在“Ann. Sci.Éc. Norm. Supér.”、“Ann. PDE”、“Comm. Math. Phys.”、“Arch. Ration. Mech. Anal.”、“Math. Ann.”等国际主流数学杂志发表多篇学术论文。

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