  This paper presents the first ever systematic theoretical formulation
addressing the long-standing open issue of regularization of the singularity
associated with the Parker sonic critical point in the linear perturbation
problem for Parker's unsteady solar wind model. This development recognizes the
necessity to go outside the framework of the linear perturbation problem and
incorporate the dominant nonlinearities in this dynamical system. This task is
accomplished by constructing a whole new theoretical formulation of Parker's
unsteady solar wind model based on the potential flow theory in ideal gas
dynamics, which provides an appropriate optimal theoretical framework for this
purpose. The stability of Parker's steady solar wind solution is shown to
extend also to the neighborhood of the Parker sonic critical point by going to
the concomitant nonlinear problem.
