A nouveau sur les équations de Stokes et de Navier-Stokes avec des conditions aux limites sur la pression. (Going back to Stokes and Navier- Stokes equations with boundary conditions on the pressure). (French) Zbl 0613.76029

In a previous note [see the review above (Zbl 0613.76028)] we introduced boundary conditions on the pressure for the Stokes equations. In this note we derive a new variational formulation for this problem and two cases of not necessarily simply connected domains are treated. In the first case, the data fix the velocity and the pressure. In the second case, the data must verify a compatibility condition, but the fluxes of the velocity can be choosen arbitrarily. Some results are extended to Navier-Stokes equations. Numerical results are presented.


76D07 Stokes and related (Oseen, etc.) flows
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations


Zbl 0613.76028