The heat convection in a rotating tube

The unsteady boundary value fluid motion problem in the rotating cylindrical tube is investigated. There are no mass forces, since it is assumed that the angular velocity of the cylinder rotation is high enough. The Oberbeck—Boussinesq equations are used to describe the fluid motion. From the mathematical point of view, the problem is inverse with respect to the pressure gradients along the cylinder axis. Based on the priori estimates, conditions are obtained under which the stationary inverse problem solution is exponentially stable. In Laplace images, the solution is found in the form of quadratures. Sufficient conditions are given for the non-stationary problem solution to reach the stationary mode with increasing time.