报告题目: Commutator estimates on bounded domains and applications to IBVP to compressible Navier-Stokes equations
报 告 人:李进开 教授 华南师范大学
报告时间:2023年12月24日(星期日) 15:05-15:55
报告地点:海山楼(创新园大厦)B1410
校内联系人:曹杨、王文栋 联系电话:84708351-8139
报告摘要:In this talk, we will present estimates on two kinds of commutators defined on bounded domains: one is a natural extension in the case of general bounded domains of the classic Riesz commutator and the other is that of the spatial derivatives with the solution mapping of the co-normal derivative problem of the Laplacian. These two kinds of commutators arise in studying the IBVP to the compressible Navier-Stokes equations with Navier slip boundary conditions. As an application of these commutator estimates as well as a BMO estimate for the gradient of solutions to the Lame system subject to the Navier slip boundary conditions, we establish the global well-posedness of strong solutions to the isentropic compressible Navier-Stokes equations with general Navier slip boundary conditions on general boundary domains, under the condition that the initial energy is small. The initial vacuum is allowed.
报告人简介:李进开,华南师范大学必赢3003am院长,教授,博士生导师。2022年入选“国家高层次人才特殊支持计划”科技创新领军人才,2018年入选“国家海外高层次人才引进计划”青年项目,曾获得“2020世界华人数学家联盟最佳论文奖”金奖(2020 ICCM Best Paper Award)以及“第二届中国科协优秀科技论文”奖,被授予第二十五届广东省青年五四奖章。目前已在包括CPAM, Adv. Math, JFA, ARMA, CPDE, SIMA等国际学术期刊上发表SCI论文40多篇。