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In general the solutions to the azimuthal equations of motion of the solar wind possess a singularity at the radial Alfvenic critical point if the fluid is non-viscous and has an infinite electrical conductivity. This singularity can only be removed by a proper choice of boundary conditions. If a plasma with a large but finite conductivity is considered, the singularity is removed in the mathematical sense. However, it is shown that for this latter case the actual solution does not differ significantly from the former model and that the boundary condition is still determined from the behavior of the solution at or near the Alfvenic critical point.

A model of the solar atmosphere is presented in which we discuss the conservation of angular momentum for the two basic states in which the solar gas can be: namely, either confined by closed field lines or outflowing along open magnetic field lines. It can be shown that the boundary conditions are in general different for these two cases. From this we obtain the results that in the closed configuration the gas can corotate at the solar surface with the magnetic field lines and its angular velocity will then increase with height, whereas for a gas flowing along an open field line the angular velocity will decrease. An exception to the latter case can be found where the open magnetic field lines are strongly nonradial and where the density is a slowly varying function of radius. In such regions the angular velocity may initially increase with height, reach a maximum and then decrease.

The solutions of a radially symmetrical solar wind model with thermal conductivity are discussed in the neighborhood of the loci of the critical points, called the critical line, and at infinity. It is shown that for constant mass and total energy flux the conditions at infinity are related uniquely to the conditions at the critical line. Furthermore the requirement that the solution is continuous and has the proper behavior at infinity will determine uniquely one specific point on the critical line through which the solution has to pass.