Analysis of Fluids and Related Topics: Homogeneous solutions of stationary incompressible Navier–Stokes equations with isolated singularities on the unit sphere, Yanyan Li, Rutgers University

Analysis of Fluids and Related Topics
  • Yanyan Li
  • Rutgers University
  • Homogeneous solutions of stationary incompressible Navier–Stokes equations with isolated singularities on the unit sphere
Oct 4, 2018
4:30 pm
Fine Hall 322

Speaker: Yanyan Li, Rutgers University

Abstract:

We classify all (−1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier– Stokes equations in three 
dimension which are smooth on the unit sphere minus the south and north pole.   They are parameterized as a 4-dimensional surface with boundary. 
We prove the existence of (−1)-homogeneous axisymmetric solutions with nonzero swirls near  the interior and one part of the boundary of the solution surface, and we prove 
that there is no such solution near  the other part of the boundary.
We also analyze vanishing viscosity limit of 
(−1)-homogeneous axisymmetric no-swirl solutions.
These are joint work with Li Li and Xukai Yan.