NAVIER-STOKES EQUATIONS WITH IMPOSED PRESSURE AND VELOCITY FLUXES

Boundary value problems for Stokes and Navier-Stokes equations with no n-standard boundary conditions are studied. Included is the case where the pressure or its normal derivative is given on some part of the bo undary or the pressure is given up to a constant but given velocity fl ux. First, a variational formulation is introduced which is shown to b e equivalent to the Stokes equations with the non-standard boundary co nditions under consideration. The existence and uniqueness of the solu tion of the variational problem are studied. Secondly, most of the res ults obtained for the Stokes equations are extended to the case of the Navier-Stokes equations. The final section is devoted to numerical ex periments, flows in pipes and physiological flows.