Nonlinear Partial Differential Equations

Date: November 17, 2020

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Gieri Simonett, Vanderbilt University

Title: On the Navier-Stokes equations on surfaces

Abstract: I will consider the motion of an incompressible viscous fluid on a compact surface without boundary. Local-in-time well-posedness is established in the framework of Lp-Lq-maximal regularity. It will be shown that the set of equilibria consists exactly of the Killing vector fields. Moreover, it will be shown that each equilibrium is stable and that any solution starting close to an equilibrium converges at an exponential rate to a (possibly different) equilibrium as time tends to infinity.