报告题目：Homogeneous solutions of stationary incompressible Navier-Stokes equations with singular rays
报 告 人：闫绪恺（俄克拉荷马州立大学数学系助理 教授）
报告地点：腾讯会议ID：865 530 063
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.