Seminar Details
2019-09-24 (14:00) : Global Stabilization of the Navier-Stokes Equations Around an Unstable Steady State
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Abdou Sene (LANI - Laboratoire d'Analyse Numérique et Informatique [Sénégal])
Abstract :
We present a mixed (Dirichlet-Neumann) boundary feedback controller for stabilizing the Navier-Stokes equations around a prescribed steady state, in a bounded domain. The Neumann part of the boundary controller is designed to be zero when the inflow vanishes, and to have the magnitude of the kinetic energy.
An appropriate choice of the controllers allows to prove exponential decrease of the perturbation in L2, without blowup. In addition, we prove, on the one hand, that the exponential convergence towards zero holds in H1, on the other hand, that the weak solution is unique when the computational domain is two-dimensional.
The procedure we adopt is mainly based on the Galerkin discretization method, and the use of compacity results. Indeed, the stabilization is achieved first for the finite dimensional system, then we pass to the limit by exploiting compactness theory.