Regularity at a magnetosonic point
= Regularity at a magnetosonic point
If a steady wind equation has the form $(w^2-c_{\mathrm f}^2)(w^2-c_{\mathrm s}^2)w'/w=\mathcal N$, a smooth nondegenerate crossing requires $\mathcal N=0$ at the corresponding <magnetosonic critical speed>. Subsequent differentiation or the full system determines the admissible slope. The numerator condition alone does not prove that a global smooth wind exists.