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