The equation of potential flows of a compressible viscous fluid at small reynolds numbers: Existence, uniqueness, and stabilization of solutions

We consider the system of equations for the motion of a compressible fluid at small Reynolds numbers. In the class of potential flows, the system is reduced to a single third order equation for the velocity potential. Existence and uniqueness theorems in various functional spaces are proved for a solution to the original initial-boundary value problem and estimates are given for the stabilization rate at infinite time.