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甬江数学讲坛187讲(2021年第46讲)
2021-09-29 09:19     (点击:)

报告题目:Homogeneous solutions of stationary incompressible Navier-Stokes equations with singular rays

人:闫绪恺(俄克拉荷马州立大学数学系助理 教授)

报告时间:2021930 上午9:00开始

报告地点:腾讯会议ID865 530 063

或点击链接入会:https://meeting.tencent.com/dm/SLF4VReHv3na

报告摘要:In 1944, Landau discovered a three parameter family of explicit (-1)-homogeneous solutions of 3D stationary incompressible Navier-Stokes equations (NSE) with precisely one singularity at the origin, which are axisymmetric with no swirl. These solutions are now called Landau solutions. If a (−1)-homogeneous solution is smooth on the unit sphere, Sverak proved that it must be a Landau solution.  This talk focuses on (-1)-homogeneous solutions of 3D incompressible stationary NSE with finitely many singular rays. I will first discuss the existence and classification of  such solutions that are axisymmetric with two singular rays passing through the north and south poles. We classify all such solutions with no swirl and then obtain existence of nonzero swirl solutions through perturbation methods. I will then describe the asymptotic expansions of such solutions near a singular ray. I will also establish the asymptotic stability for some of the axisymmetric no-swirl solutions we obtained. This is a joint work with Li Li and Yanyan Li.

报告人简介:闫绪恺,美国俄克拉荷马州立大学数学系助理教授。其在中国科学技术大学取得学士学位,随后于美国罗格斯大学取得博士学位,并在佐治亚理工大学从事博士后研究。2020年至今就职于俄克拉荷马州立大学。主要从事非线性偏微分方程的研究。

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