應yl7703永利官網耿俊教授和王躍循教授邀請，清華大學數學科學系何凌冰教授將于2022年9月30日上午在線舉辦學術報告。

報告題目:Global strong solutions of 3D Compressible Navier-Stokes equations with short pulse type initial data

時 間：9月30日（星期五）10：00

騰訊會議ID：871 175 104

報告摘要：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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何凌冰教授簡介

何凌冰，清華大學數學科學系教授、博士生導師。何凌冰教授主要從事流體力學和動理學偏微分方程的理論研究，在相關課題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.”等國際重要學術期刊上發(fā)表論文多篇。

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