主办单位：英国威廉希尔公司官网基础数学研究中心

报告内容简介：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 otal energy, and great difficulties associated with both local and global well-posedness of strong solutions. In particular, ince the entropt is one of the most important physical states and it's 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, and Qin Duan - 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突出贡献。辛周平教授是美国Sloan Research Fellow、教育部国家级人才，MAA主编，JMP和M2AS副主编，M3AS和SCM等杂志的编委。他曾任香港数学会会长，获得的许多荣誉包括：世界华人数学家大会“晨兴数学奖金奖”（2004年）、国际数学家大会特邀报告人（2002年）、美国“Sloan奖”（1991年）等。