报告时间：2023年9月22日（星期五）14:30-15:30

报告地点：腾讯会议489-462-368

报告人：何凌冰 教授

工作单位：清华大学

举办单位：数学学院

报告简介：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 allowthe 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.

报告人简介：何凌冰，清华大学教授，2007年毕业于中科院数学与系统科学研究院。主要研究碰撞型动理学方程的适定性理论以及方程间的渐近关系。