报告题目：Global regularity and decay behavior for Leray equations with 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 this talk, we show the global regularity and the optimal decay of weak solutions to the generalized Leray problem with critical dissipation. Our method is based on the maximal smoothing effect, W2, p-type theory of linearization, and the action of the heat semigroup generated by the fractional powers of Laplace operator on distributions with Fourier transforms supported in an annulus. As a by-product, we shall construct a self-similar solution to the tree-dimensional Navier-Stokes equations, and more importantly, prove the global regularity and the optimal decay without 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. Math.、Arch. Ration. Mech. Anal.、Comm. Math. Phys.、Trans. AMS、J. Math. Pures Appl.、Rev Mat Iberoan、SIAM J. Math. Anal.、 等在内的重要学术期刊。