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Article Contents

# Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. Ⅲ. Two singularities

• * Corresponding author: Xukai Yan

Dedicated to Luis Caffarelli on his 70th birthday, with admiration and friendship

The first named author is partially supported by NSFC grants 11871177. The second named author is partially supported by NSF grants DMS-1501004. The third named author is partially supported by AMS-Simons Travel Grant and AWM-NSF Travel Grant 1642548

• 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.

Mathematics Subject Classification: Primary: 35Q30, 76D03; Secondary: 76D05.

 Citation:

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