报告题目：Global small solution and decay to some fluid mechanics systems
报告人：许孝精 教授（北京师范大学）
报告时间：2020年7月17日（周五）下午15:00-16:00
腾讯会议ID：191 177 013
报告摘要：In this talk, I shall introduce the stability and large-time behavior problems on perturbations near the trivial solution to some fluid mechanics systems. These systems do not involve dissipation terms. These stability problems are extremely difficult, partially due to the lack of dissipation. The energy method and classical approaches can no longer provide information on the large-time behavior of these partially dissipated systems. We will presents a new approach that take into account of the special structure of the linearized system. The linearized parts of the systems here both obey a degenerate damped wave type equations. By representing the nonlinear system in an integral form and carefully crafting the functional setting for the initial data and solution spaces, we are able to establish the long-term stability and global (in time) existence and uniqueness of smooth solutions of the nonlinear systems focused here. Simultaneously, we also obtain exact decay rates for various derivatives of the perturbations.
报告人简介：许孝精，男，北京师范大学数学科学学院教授，副经理。2005年于吉林大学获得博士学位。主要研究流体动力学中偏微分方程组的适定性理论。博士学位论文获“吉林省优秀博士学位论文”，曾获北京师范大学励耘优秀青年教师一等奖。主持完成省部级及以上的科研项目多项。完成学术论文50余篇，部分结果发表在J. Math. Pures Appl., SIAM J. Math. Anal.，Nonlinearity，J. Nonlinear Science，J. Differential Equations等知名杂志上，被引用500余次。曾在法国、美国、加拿大、波兰和香港等地区进行学术访问十余次。
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