| Abstract: |
| In this talk, we study the stationary Stokes and Navier--Stokes equations in an $L^p$ framework under mixed Navier-type boundary conditions, combining Dirichlet conditions on part of the boundary with prescribed normal trace and tangential vorticity on the complementary part.
A central aspect of this work is the precise characterization of the dual spaces associated with divergence-free function spaces adapted to these boundary conditions. This duality framework allows for a rigorous variational formulation beyond the Hilbert setting.
As an application, we establish the existence of weak and strong solutions in the $L^p$ theory for both the Stokes and Navier--Stokes systems under these mixed boundary conditions. |
|