An Initial-Boundary Value Problem for a Viscous Compressible Flow

A constructive approach is presented to treat an initial boundary value problem for isothermal Navier–Stokes equations. It is based on a characteristics (Lagrangean) approximation locally in time and a boundary integral equation method via nonstationary potentials. As a basic problem, the latter leads to a Volterra integral equation of first kind which is proved to be uniquely solvable and even coercive in some anisotropic Sobolev spaces. The solution depends continuously upon the data and can be constructed by a quasioptimal Galerkin procedure.