PRESSURE STABILIZATION METHOD FOR STEADY VISCOUS FLOWS IN A SYSTEM OF PIPES

摘要

This paper deals with a singular perturbation of the stationary Stokes and Navier-Stokes systems. The term ε~2Δp is added to the continuity equation, where ε is a small parameter. For a domain with cylindrical outlets to infinity and exponentially decaying data, existence and uniqueness of solutions under flux conditions at infinity are established for the linear problem and also for the nonlinear problem in the case of small data. Asymptotically exact estimates are proved for ε tending to zero. For sufficiently regular data, these estimates imply the convergence in H_(loc)~(5/2-δ) for the velocity parts and in H_(loc)~(3/2-δ) for the pressure parts, respectively.