Strong Null Structure of Fluid PDEs
报 告 人:: 雷震
报告地点:: 数学与统计学院104报告厅
报告时间:: 2018年10月09日星期二09:30-10:30
报告简介:

We introduce the concept of strong null condition and discovered that incompressible fluid PDEs inherently satisfy such a condition. Analytically such a structure plays a crucial role in imporving the time decay rate of good unknowns. As a consequence, we are able to prove the global stability of incompressible elastodynamics in two dimensions which was a long-standing open question (Lei, 2016). Moreover, such a structure is also revealed to be crucial in the study of global vanishing viscosity limit. This is a key topics in both the theory of fluid mechanics and the analysis of partial differential equations. In general, as long as the time is global, the verification of such a theory is highly nontrivial and is thus open for most fluid systems. In the second part, we report our recent results on the global vanishing limit of incompressible viscoelasticity (joint with Yuan Cai, Fanghua Lin and Nader Masmoudi, preprint) and MHD (joint with Yuan Cai, 2018).

举办单位:数学与统计学院
发 布 人:吴双 发布时间: 2018-10-08
主讲人简介:
雷震,河南商城人,2001年本科毕业于东北师范大学,现任复旦大学数学科学院教授、副院长,曾为美国普林斯顿高级研究院member。雷震教授的主要研究方向为偏微分方程及其控制理论。他提出了“强零条件”的概念,独立证明了二维不可压弹性力学方程平衡态附近经典解的整体存在性,曾获上海市自然科学牡丹奖、优青、青年拔尖、青年长江、国家杰青及科技部中青年科技创新领军人才等荣誉。