“数学及其应用”重点实验室年会特邀报告——关于三维各向异性Navier-Stokes方程的整体解
报告人：张平 院士
时间：2022-12-10 9:40-10:40
地点：腾讯会议：734-737-203 会议密码：221210
报告摘要：
In this paper, we first prove the global existence of strong solutions to 3-D incompressible Navier-Stokes equations with solenoidal vector field initial data, which writes in the cylindrical coordinate is of the form: ${\rm A}(r,z)\cos N\th +{\rm B}(r,z)\sin N\th,$ provided that $N$ is large enough.
The main idea of the proof is to write the solution in the trigonometrical series in the $\th$ variable and estimate the coefficients separately in some scaling invariant spaces. We remark that the most crucial step to derive the classical {\it a priori} estimate of the solution is to handle a sort weighted sum of the norms of the coefficients. Then we extend the above well-posedness result for initial data which is linear combinations of axisymmetric initial without swirl and infinite high mode trigonometric series in the angular variable.
嘉宾介绍：
张平，现任中科院数学与系统科学研究院副经理，中国科学院院士。曾于2005年获国家杰出青年基金；2007年获第十届中国青年科技奖; 2011年获国家自然科学二等奖；2014年获聘国家重大人才计划特聘教授；2019年获中国数学会陈省身奖等奖项，2021年被评为中国科学院院士。自1997年以来，共在Comm. Pure Appl. Math.，Ann. Sci. École Norm. Sup., Arch. Ration. Mech. Anal.， Comm. Math. Phys.，Adv. Math.， J. Reine Angew. Math.等杂志发表文章110余篇，在美国数学会出版专著一本。主要研究领域为粘性不可压缩流体力学方程组与非线性Schraedinger方程的半经典极限。
