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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）

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 $\delta^{-\f{\alpha}{\gamma}}$ 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.

报告时间：2023年4月21日（周五）上午10:00-11:00

报告地点：教二楼913教室

联系人：牛冬娟