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

Abstract:

In this seminar, we will examine the well-posedness of the Stokes problem when both the velocity and pressure are required to vanish on the domain boundary. Our analysis shows that the pressure must vanish in a narrow band near the boundary, and we establish well-posedness by extending Nečas' inequality to such square-integrable functions. We also find that the a priori estimate for pressure depends inversely on the size of this band. Numerical experiments confirm these findings. Based on our findings, we will provide practical guidelines for applying vanishing pressure boundary conditions in PDE model coupling, particularly for ice sheet simulations.