报告题目：On regular solutions for three-dimensional full compressible Navier-Stokes equations with degenerate viscosities and far field vacuum(一)、(二)

报 告 人：朱圣国，上海交通大学数学科学学院副教授、博导

报告时间：2023年3月20日（周一）14:00-16:00

会议地点：20幢404（第一会议室）

报告摘要：The Cauchy problem for the 3-D full degenerate compressible Navier-Stokes equations with far field vacuum is considered. First, when shear and bulk viscosity coefficients  both depend on the absolute temperature in a  power law of Chapman-Enskog,  based on some elaborate analysis of this system’s intrinsic singular structures, we identify one class of initial data admitting a local-in-time regular solution with far field vacuum in terms of the mass density, velocity and  entropy . Furthermore, it is shown that within its life span of  such a regular  solution, the velocity  stays in an inhomogeneous Sobolev space, the entropy has uniformly  finite lower and upper bounds in the whole space, and  the laws of  conservation of  total mass, momentum and  total energy are all satisfied. Note that  due to the appearance  of the vacuum, the momentum equations are  degenerate both in the time evolution and viscous stress tensor,  and the physical entropy for polytropic gases behaves singularly, which make the  study on corresponding  well-posedness challenging. For  proving  the existence,  we first  introduce    an   enlarged reformulated structure by considering  some new variables, which  can transfer the degeneracies  of the full CNS   to the possible singularities of some special source terms related with the entropy, and then carry out some  singularly weighted energy estimates carefully designed  for this reformulated system. This talk is based on a joint work with Dr. Qin Duan and Prof. Zhouping Xin.

报告人简介：朱圣国，男，上海交通大学数学科学学院副教授、博导。2015年于上海交通大学获理学博士学位。毕业之后先后在香港中文大学、澳大利亚莫纳什大学、英国牛津大学做博士后。2020年返回上海交大任教。主要从事与流体力学及相对论相关的非线性偏微分方程的理论研究工作，在可压缩Navier-Stokes 及Euler方程组的适定性和奇异性方面取得了一系列重要进展。目前已在国际学术期刊上发表学术论文30余篇，其中包括Transactions of the AMS、Advances in Mathematics、Arch. Ration. Mech. Anal.、Ann. Inst. H. Poincare Anal. Non Lineaire、J. Math. Pures Appl. 等本领域权威杂志。 并于2017年入选英国皇家学会“Newton International Fellow”; 2019年入选中组部国家海外高层次人才引进计划（青年项目）；2020年入选上海市海外高层次人才引进计划。 目前主持科技部国家重点研发计划一项。

邀请人：赖宁安，耿金波