Analytical and numerical investigation of unsteady flow near a critical point

The problem of unsteady flow of a viscous incompressible fluid near a critical point on a plane boundary is investigated. A theorem on the existence and uniqueness of its solution in Hölder classes of functions on an arbitrary time interval with natural restrictions imposed on the initial function is proved. Qualitative properties of the solution are investigated. Results of a numerical analysis demonstrating the possibility of disappearance after a finite time of a counterflow zone existing at the initial time in the case of a negative pressure gradient at the rigid plane are presented. In the case when the pressure gradient is a periodic function, a periodic mode of motion as well as breakdown of the solution after a finite time is possible.