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We classify all (-1)-homogeneous axisymmetric no-swirl solutions ofincompressible stationary Navier-Stokes equations in three dimension which aresmooth on the unit sphere minus the south and north poles, parameterizing themas a four dimensional surface with boundary in appropriate function spaces.Then we establish smoothness properties of the solution surface in the fourparameters. The smoothness properties will be used in a subsequent paper wherewe study the existence of (-1)-homogeneous axisymmetric solutions with non-zeroswirl on $\mathbb{S}^2\setminus\{S,N\}$, emanating from the four dimensionalsolution surface.

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