报告题目：Some Recent Results on Compressible Navier-Stokes Equations

报 告 人：李竞 研究员 中科院数学与系统科学研究院、南昌大学

报告时间：2022年6月20日 星期一 下午15:30-16:30

报告地点：腾讯会议 ID：619-476-801

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校内联系人：王春朋 wangcp@jlu.edu.cn

报告摘要：We investigate the barotropic compressible Navier-Stokes equations with slip boundary conditions in a three-dimensional (3D) simply connected bounded domain, whose smooth boundary has a finite number of two-dimensional connected components. For any adiabatic exponent bigger than one, after obtaining some new estimates on boundary integrals related to the slip boundary conditions, we prove that both the weak and classical solutions to the initial-boundary-value problem of this system exist globally in time provided the initial energy is suitably small. Moreover, the density has large oscillations and contains vacuum states. Finally, it is also shown that for the classical solutions, the oscillation of the density will grow unboundedly in the long run with an exponential rate provided vacuum appears (even at a point) initially. This is the first result concerning the global existence of classical solutions to the compressible Navier-Stokes equations with density containing vacuum states initially for general 3D bounded smooth domains. This is a joint work with Guocai Cai (Xiamen University).

报告人简介：李竞，中科院数学与系统科学研究院研究员，国家杰出青年基金获得者，南昌大学特聘教授、博士生导师，现任南昌大学数学与交叉科学研究院经理。2004年8月香港中文大学数学专业博士毕业，2015年获国家杰出青年科学基金，2018年获得首届世界华人数学家联盟大会(ICCM)五年最佳论文银奖，入选江西省“双千计划”创新领军人才。主要研究方向为可压缩Navier-Stokes方程，证明了三维空间可压缩Navier-Stokes方程含真空的大震荡古典解的整体存在性等一系列重要结果，研究工作发表在Comm. Pure Appl. Math.、Arch. Ration. Mech. Anal.、Comm. Math. Phys. 等国际著名数学杂志，论文被引用1100余次。