Seminar

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Abstract:

We shall present two main recent (2020) results, joint with Irena Lasiecka and Buddhika Priysad. First, the 3D-Navier-Stokes equations can be uniformly stabilized in the vicinity of an unstable equilibrium solution by means of a ’minimally’ invasive, localized, boundary-based, tangential, static, feedback control strategy, which moreover is finite dimensional. Finite dimensionality in 3D was an open problem. Its solution required a new, suitable, tight Besov space setting of low regularity. Next, the 3D Boussinesq system can likewise be uniformly stabilized near an unstable equilibrium pair by a finite dimensional static, feedback control strategy. This includes a scalar localized feedback control acting on the boundary of the thermal component; and a localized interior feedback control acting on the Navier-Stokes component, that moreover can be taken of reduced dimension (3 -1)=2. In both cases, the finite dimensional stabilizing controllers are obtained constructively. Moreover, in both cases, suitable unique continuation properties of suitably overdetermined adjoint eigenproblems play a critical role.

Boundary Feedback Stabilization of Fluids in Besov Spaces of Low Regularity by Means of Finite Dimensional Controllers 3D Navier