Homogeneous solutions of stationary Navier–Stokes equations with isolated singularities on the unit sphere. II. Classification of axisymmetric no-swirl solutions

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 poles, parameterizing them as a four dimensional surface with boundary in appropriate function spaces. Then we establish smoothness properties of the solution surface in the four parameters. The smoothness properties will be used in a subsequent paper where we study the existence of (−1)-homogeneous axisymmetric solutions with non-zero swirl on S2∖{S,N}, emanating from the four dimensional solution surface.