35:37
publiée le 8 avril 2024
On the Radon-Carleman problem in uniformly rectifiable domains
De Irina Mitrea
On the Navier-Stokes equations on surfaces
Apparaît dans la collection : Jean-Morlet Chair 2022 - Conference: Nonlinear PDEs in Fluid Dynamics / Chaire Jean-Morlet 2022 - Conférence : EDP non-linéaires en dynamique des fluides
I will consider the motion of an incompressible viscous fluid on compact surfaces without boundary. Local in time well-posedness is established in the framework of $L_{p}$-$L_{q}$ maximal regularity for initial values in critical spaces. It will be shown that the set of equilibria consists exactly of the Killing vector fields. Each equilibrium is stable and any solution starting close to an equilibrium converges at an exponential rate to a (possibly different) equilibrium. In case the surface is two-dimensional, it will be shown that any solution with divergence free initial value in $L_{2}$ exists globally and converges to an equilibrium.
