题 目：Homogeneous solutions of stationary incompressible Navier-Stokes equations with singular rays

报告人：Yanyan Li （Rutgers University and Beijing Normal University）

Abstract: Landau discovered explicit (-1)-homogeneous solutions of 3-d stationary incom- pressible Navier-Stokes equations with precisely one singularity at the origin. These solu- tions are axisymmetric with no swirl. Sverak proved in 2006 that these are the only (-1)- homogeneous solutions with one singularity, while Gang Tian and Zhouping Xin proved in 1998 the result under an additional axisymmetry assumption on solutions. Sverak also proved that there are no such solutions in dimension bigger than 3.

We construct various (-1)-homogeneous solutions of stationary incompressible Navier- Stokes equations with finite singular rays. For instance, we obtain a three parameter family of (-1)-homogeneous, axisymmetric solutions with nonzero swirl of 3-d stationary incompress- ible Navier-Stokes equations which are singular only on a single ray. We will also present asymptotic behavior of general (-1)-homogeneous axisymmetric solutions near an isolated singular ray. This is a joint work with Li Li and Xukai Yan

时间：7月21日（周四）下午4：00 - 5：00

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