HOMOGENEOUS SOLUTIONS OF STATIONARY NAVIER-STOKES EQUATIONS WITH ISOLATED SINGULARITIES ON THE UNIT SPHERE. Ⅲ . TWO SINGULARITIES

摘要

All (-1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus north and south poles have been classified in our earlier work as a four dimensional surface with boundary. In this paper, we establish near the no-swirl solution surface existence, non-existence and uniqueness results on (-1)-homogeneous axisymmetric solutions with nonzero swirl which are smooth on the unit sphere minus north and south poles.