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，华南师范大学数学科学学院院长，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。