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Home » Euler/Navier Stokes (Part 1): Boundary Feedback Stabilization of Fluids in Besov Spaces of Low Regularity by Means of Finite Dimensional Controllers: 3D Navier-Stokes Equations and Boussinesq Systems

Seminar

Euler/Navier Stokes (Part 1): Boundary Feedback Stabilization of Fluids in Besov Spaces of Low Regularity by Means of Finite Dimensional Controllers: 3D Navier-Stokes Equations and Boussinesq Systems May 27, 2021 (08:00 AM PDT - 09:00 AM PDT)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Roberto Triggiani (University of Memphis)
Description

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

 

 

Video
Abstract/Media

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.

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