Finite-dimensional boundary uniform stabilization of the Boussinesq system in Besov spaces by critical use of Carleman estimate-based inverse theory

DOI10.1515/jiip-2020-0132OpenAlexW3150261101MaRDI QIDQ2075140

Buddhika Priyasad, Roberto Triggiani, Irena Lasiecka

Publication date: 14 February 2022

Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.03262

zbMATH Keywords

Besov spaceboundary stabilizationBoussinesq systeminverse theory

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Stabilization of systems by feedback (93D15) Smoothness and regularity of solutions to PDEs (35B65) Heat equation (35K05) Inverse problems for PDEs (35R30) Navier-Stokes equations (35Q30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs in connection with classical thermodynamics and heat transfer (35Q79) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Diffusive and convective heat and mass transfer, heat flow (80A19)

Cites Work

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• Boundary controllability of incompressible Euler fluids with Boussinesq heat effects
• Local null controllability of the three-dimensional Navier-Stokes system with a distributed control having two vanishing components
• Minimal initial data for potential Navier-Stokes singularities
• The existence and uniqueness of very weak solutions of the stationary Boussinesq system
• Unique continuation from an arbitrary interior subdomain of the variable-coefficient Oseen equation
• Unique continuation of boundary over-determined Stokes and Oseen eigenproblems
• Weighted Schauder estimates for evolution Stokes problem
• Boussinesq system with non-homogeneous boundary conditions
• Null controllability of the \(N\)-dimensional Stokes system with \(N - 1\) scalar controls
• Semigroups of linear operators and applications to partial differential equations
• Domains of fractional powers of the Stokes operator in \(L_ r\) spaces
• Boundary feedback stabilizability of parabolic equations
• Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations
• Analyticity of the semigroup generated by the Stokes operator in \(L_r\) spaces
• On the stabilizability problem in Banach space
• Estimates for solutions of nonstationary Navier-Stokes equations
• On the solvability of boundary and initial-boundary value problems for the Navier-Stokes system in domains with noncompact boundaries
• Boundary layers on Sobolev-Besov spaces and Poisson's equation for the Laplacian in Lipschitz domains
• Stabilization for the 3D Navier-Stokes system by feedback boundary control.
• On the strong solvability of the Navier-Stokes equations
• Boundary feedback stabilization of the Boussinesq system with mixed boundary conditions
• Stabilization of the Boussinesq equation via internal feedback controls
• Carleman estimates for coefficient inverse problems and numerical applications.
• Stationary solutions for generalized Boussinesq models
• Stabilization of Navier-Stokes flows.
• Feedback stabilization of a thermal fluid system with mixed boundary control
• Uniform stabilization of Navier-Stokes equations in critical \(L^q\)-based Sobolev and Besov spaces by finite dimensional interior localized feedback controls
• Uniform stabilization of Boussinesq systems in critical \(\mathbf{L}^q \)-based Sobolev and Besov spaces by finite dimensional interior localized feedback controls
• Unique continuation properties of over-determined static Boussinesq problems with application to uniform stabilization of dynamic Boussinesq systems
• Stabilization to an equilibrium of the Navier-Stokes equations with tangential action of feedback controllers
• Abstract settings for tangential boundary stabilization of Navier--Stokes equations by high- and low-gain feedback controllers.
• Local exact controllability to the trajectories of the Boussinesq system
• Maximal regularity for the Stokes system on noncylindrical space-time domains
• The Boussinesq system with mixed nonsmooth boundary data
• Un'applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine
• Moving Interfaces and Quasilinear Parabolic Evolution Equations
• Minimal $L^3$-Initial Data for Potential Navier--Stokes Singularities
• Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems
• Solutions to a Free Boundary Problem of Fluid-Structure Interaction
• On the Feedback Stabilization of Boussinesq Equations
• An Introduction to the Mathematical Theory of the Navier-Stokes Equations
• Convexification for a Three-Dimensional Inverse Scattering Problem with the Moving Point Source
• Uniform Stabilization with Arbitrary Decay Rates of the Oseen Equation by Finite-Dimensional Tangential Localized Interior and Boundary Controls
• Linear independence of boundary traces of eigenfunctions of elliptic and Stokes operators and applications
• Determination of the Solutions of the Navier-Stokes Equations by a Set of Nodal Values
• Elliptic boundary value problems in unbounded domains with noncompact and nonsmooth boundaries
• Stability estimates for ill-posed cauchy problems involving hyperbolic equations and inequalities
• On the existence and uniqueness of the stationary solution to equations of natural convection with boundary data in L ²
• L^ptheory for Boussinesq system with Dirichlet boundary conditions
• L_3,∞-solutions of the Navier-Stokes equations and backward uniqueness
• $L^{p}$-theory for strong solutions to fluid-rigid body interaction in Newtonian and generalized Newtonian fluids
• Convexification and experimental data for a 3D inverse scattering problem with the moving point source
• Tangential boundary stabilization of Navier-Stokes equations
• Estimates of the solutions of a nonstationary linearized system of Navier-Stokes equations
• Internal stabilization of Navier-Stokes equations with finite-dimensional controllers
• Inverse problems for partial differential equations
• Mathematical control theory: an introduction
• Solvability and maximal regularity of parabolic evolution equations with coefficients continuous in time
• Maximal regularity in \(L^p\) spaces for an abstract Cauchy problem