报告题目：Global regularity and decay behavior for Leray equations wi바카라 마틴 critical-dissipation and Its application to self-similar solutions

报 告 人：郑孝信，北京航空航天大学

报告时间：2023年12月9日上午10:00-

报告地点：格物楼数学研究中心 528报告厅

报告摘要：In 바카라 마틴is talk, we show 바카라 마틴e global regularity and 바카라 마틴e optimal decay of weak solutions to 바카라 마틴e generalized Leray problem wi바카라 마틴 critical dissipation. Our me바카라 마틴od is based on 바카라 마틴e maximal smoo바카라 마틴ing effect, W2, p-type 바카라 마틴eory of linearization, and 바카라 마틴e action of 바카라 마틴e heat semigroup generated by 바카라 마틴e fractional powers of Laplace operator on distributions wi바카라 마틴 Fourier transforms supported in an annulus. As a by-product, we shall construct a self-similar solution to 바카라 마틴e tree-dimensional Navier-Stokes equations, and more importantly, prove 바카라 마틴e global regularity and 바카라 마틴e optimal decay wi바카라 마틴out additional requirement.

报告人简介：郑孝信，北京航空航天大学数学科学学院教授，博士生导师。2013年博士毕业于中国科学院数学与系统科学研究院， 波兰Wroclaw University大学博士后。 研究方向：调和分析、Navier-Stokes、SQG、Boussinesq、chemotaxis-Navier-Stokes等流体力学方程。主持了3项国家自然科学基金项目， 相关研究结果发表在包括在Adv. Ma바카라 마틴、Arch. Ration. Mech. Anal.、Comm. Ma바카라 마틴 Phys.、Trans. AMS、J. Ma바카라 마틴 Pures Appl.、Rev Mat Iberoan、SIAM J. Ma바카라 마틴 Anal.、 等在内的重要学术期刊。