An Initial-Boundary Value Problem for the 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 intergral equation method via nonstationary potentials. As a basic problem, the later leads to a Volterra integral equation of the first kind which is proved to be uniquely solvable and even coercive in some anistropic Sobolev spaces. The solution depends continuously upon the data and may be constructed by a quasioptimal Galerkin procedure.
boundary integral equations, fundamental solution, coercivity, Korn's inequality, anistropic Sobolev spaces, variational formulation, weak solution