报告题目1：On Entropy Bounded Strong Solutions to The Compressible Navier-Stokes Equations with Far Fields Vacuum Part1

报告人：香港中文大学辛周平教授

报告时间：2023年06月10日（周六）上午10：00-12：00

报告地点：数学科学学院20-306 （腾讯会议号：579-197-321）

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 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 temperature-dependent viscosity case. The emphasize will be on the degenerate case. This talk is based on joint works with Jinkai Li, and Qin Duan - Shengguo Zhu.

报告题目2：On Entropy Bounded Strong Solutions to The Compressible Navier-Stokes Equations with Far Fields Vacuum Part2

报告人：香港中文大学辛周平教授

报告时间：2023年06年10日（周六）下午15：00—17：00

报告地点：数学科学学院20-306（腾讯会议号：727-650-958）

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 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 temperature-dependent viscosity case. The emphasize will be on the degenerate case. This talk is based on joint works with Jinkai Li, and Qin Duan - Shengguo Zhu.

报告人简介： 辛周平教授是香港中文大学数学系首席教授，香港中文大学数学科学研究所副所长,非线性科学研究中心主任。著名数学家，晨兴数学金奖获得者（2004），国际数学数学家大会45分钟报告邀请报告人（2002）。研究领域涉及偏微分方程、流体动力学方程、非线性波、数值分析，在双曲型守恒律、流体动力学和数值分析等研究方向取得了非常突出的成就，并在一维激波、高维激波、粘性激波、等领域做出了具有国际影响的研究成果。由于他在其研究领域的突出成就，1991年4月获得了美国“Sloan奖”（美国优秀博士后奖), 1993年9月获得了美国为杰出青年颁发的“美国总统奖”。2002年辛周平教授被邀请在国际数学家大会上做报告，2004年举办的“国际华人数学家大会”上，辛周平教授获得了“晨兴数学奖”，这是华人数学界的最高荣誉。辛教授是美国数学会会员、SIAM会员、《分析方法与应用》主编、《亚洲数学杂志》编委、《数学学报》编委、《SIAM Journal of Mathematical Analysis》编委、《Journal of Partial Differential Equations》编委、中国晨兴研究中心学术委员会委员。

邀请人：非线性分析与PDE团队