报告题目：Global regularity and decay behavior for Leray equations with critical-dissipation and Its application to self-similar solutions
主讲人：郑孝信（北京航空航天大学）
时间：2023年12月7日14:30-15:30
腾讯会议号：628330988
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, $W^{2,p}(\RR^3)$-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.
郑孝信，北京航空航天大学数学科学学院副教授，博士生导师，博士毕业于中国工程物理研究院，波兰 Wroclaw University 大学博士后。研究兴趣是 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， 在《Adv. Math.》、《Arch. Ration. Mech. Anal.》、《Comm. Math. Phys.》、《J. Math. Pures Appl.》、《SIAM J. Math. Anal.》、《 Trans. Amer. Math. Soc.》、《J. Differential Equations》等著名期刊上发表 SCI 论文 20 余篇。
