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

讲座时间：2022年05月30日，星期一，下午4:30—6:30

腾讯会议 ID：518-327-090

讲座人：朱圣国副教授，上海交通大学数学与统计学院

讲座简介：

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).

讲座人简介：

    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。

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会议时间：2022/05/30 16:30-18:30 (GMT+08:00) 中国标准时间 - 北京

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