学术报告

报告题目：Vacuum Dynamics and Entropy for Compressible Navier-Stokes Equations

报告人：辛周平 教授

报告时间：2022年4月1日10：00—11:00

报告地点：腾讯会议803 181020

报告摘要：The dynamics of the vacuum state is one of the challenging issues for viscous and heat conductive compressible fluids which are governed by the full compressible Navier-Stokes equations (CNS). In the presence of vacuum, the CNS are strongly degenerate, which lead to many new phenomena such as instantaneous and finite blow-up of entropy bounded solutions and breakdown of either the total momentum or the total energy, and great difficulties associated with both local and global well-posedness of strong solutions. In particular, since the entropy is one of the most important physical states and its equation is highly singular near vacuum, so the propagation of boundedness of the entropy in the presence of far fields vacuum is of great importance. In this talk, I will discuss some of key issues in studying the full Navier- Stokes system and present some recent results on entropy-bounded strong solutions to the CNS with both constant viscosity and heat conductivity coefficients and the degenerate case. This talk is based on joint works with Jinkai Li, Qin Duan and Shengguo Zhu.

报告人简介：辛周平，教授，1988年在美国密歇根大学获数学博士学位，后加入美国纽约大学柯朗数学研究所并于1996年成为终身正教授。现任香港中文大学数学科学研究所常务所长、蒙民伟数学讲座教授。辛周平教授长期从事流体力学偏微分方程理论研究，在双曲守恒律、高维激波、边界层理论、混合型方程，可压流体与不可压流体方程和松弛格式等领域做出了重要的具有国际影响的研究成果，至今发表研究文章近180篇，google引用超1万2千余次，近5年google引用超4千次。辛周平教授是美国Sloan Research Fellow、教育部国家级人才。曾在2002年国际数学家大会上做45分钟报告，在2004年的“国际华人数学家大会”上获“晨兴数学奖金奖”，2019年获得第九届“秦元勋数学奖”。辛周平教授是MAA主编，JMP和M2AS副主编，M3AS和SCM等杂志的编委。曾任香港数学会会长。