报告题目：Global well-posedness of regular solutions to the 3-D isentropic compressible Navier-Stokes Equations with degenerate viscosities and vacuum

报告人：朱圣国 副教授 (上海交通大学)

报告时间：2022年6月6日（星期一）下午15：30-17：30

报告地点：腾讯会议         会议ID：983-154-407

校内联系人：王文栋 教授      联系电话：84708351-8139

报告摘要: We talk about the Cauchy problem for the 3-D isentropic compressible Navier-Stokes equations with degenerate viscosities. By introducing some new variables and making use of the `` quasi-symmetric hyperbolic"--``degenerate elliptic" coupled structure to control the behavior of the fluid velocity, we prove the global-in-time well-posedness of regular solutions with vacuum for a class of smooth initial data that are of small density but possibly large velocities. Here the initial mass density is required to decay to zero in the far field, and the spectrum of the Jacobi matrix of the initial velocity are all positive. The result here applies to a class of degenerate density-dependent viscosity coefficients, is independent of the BD-entropy, and seems to be the first on the global existence of smooth solutions which have large velocities and contain vacuum state for such degenerate system in three space dimensions. This talk is based on a joint work with Prof. Zhouping Xin (CUHK).

报告人介绍：朱圣国，上海交通大学数学科学学院副教授，博士生导师。2015年6月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、莫纳什大学、牛津大学数做博士后。曾于2017年入选英国皇家学会牛顿学者； 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。 主要研究领域为可压缩流体力学方程组，已在Adv. Math.、Arch. Ration. Mech. Anal.、Trans. Amer. Math. Soc.、J. Math. Pures Appl. 等学术期刊上发表/接收论文20余篇。