偏微分方程系列报告

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

报告人:   朱圣国 教授 （上海交通大学）

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系统性的研究进展。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青年科学家项目一项。 

报告时间: 2023.5.19(周五) 下午 4:00-5:30

报告地点: 逸夫楼1537