Igor Tominec (Stockholm University): Well-posedness of the Stokes problem under modified pressure Dirichlet boundary conditions

In this talk, I will show that the Stokes problem is well-posed when both velocity and pressure vanish on the domain boundary. This result is achieved by extending Nečas' inequality to square-integrable functions that vanish in a small band covering the boundary. It is found that the associated a priori pressure estimate depends inversely on the volume of the band. Numerical experiments confirm these findings. Based on these results, I will outline guidelines for applying vanishing pressure boundary conditions in numerical PDE model coupling and domain decomposition methods.