On the three dimensional Kelvin-Voigt fluids: global solvability, exponential stability and exact controllability of Galerkin approximations

DOI10.3934/eect.2020007zbMath1436.76008OpenAlexW2964514892WikidataQ127355269 ScholiaQ127355269MaRDI QIDQ777217

Manil T. Mohan

Publication date: 3 July 2020

Published in: Evolution Equations and Control Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/eect.2020007

zbMATH Keywords

exact controllabilityexponential stabilitySchauder's fixed point theoremHilbert uniqueness methodstationary solutionGalerkin approximationslocal monotonicityNavier-Stokes-Voigt equationsKelvin-Voigt fluids

Mathematics Subject Classification ID

Controllability (93B05) PDEs in connection with fluid mechanics (35Q35) Finite element methods applied to problems in fluid mechanics (76M10) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Statistical solutions of Navier-Stokes and related equations (76D06) Exponential stability (93D23)

Related Items (13)

Global attractors, exponential attractors and determining modes for the three dimensional Kelvin-Voigt fluids with ``Fading memory ⋮ Exact controllability of a Faedo-Galërkin scheme for the dynamics of polymer fluids ⋮ Allen-Cahn-Navier-Stokes-Voigt systems with moving contact lines ⋮ Well-posedness and invariant measures for 2D stochastic Oldroyd model of order one with pure jumps ⋮ Dynamics of complex bodies with memory and vector-valued microstructure: existence and uniqueness ⋮ Existence of weak solution to initial-boundary value problem for finite order Kelvin-Voigt fluid motion model ⋮ A phase separation model for binary fluids with hereditary viscosity ⋮ A central limit theorem and moderate deviation principle for the stochastic 2D Oldroyd model of order one ⋮ Approximate controllability of a non-autonomous evolution equation in Banach spaces ⋮ Existence and exponential behavior for the stochastic 2D Cahn-Hilliard-Oldroyd model of order one ⋮ Approximate controllability of a Sobolev type impulsive functional evolution system in Banach spaces ⋮ Strong solution to stochastic 2D nonlocal Cahn-Hilliard-Oldroyd model of order one: existence and uniqueness ⋮ A local in time existence and uniqueness result of an inverse problem for the Kelvin-Voigt fluids

Cites Work

• New methods for local solvability of quasilinear symmetric hyperbolic systems
• A simple proof of global solvability of 2-D Navier-Stokes equations in unbounded domains.
• Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models
• Global attractors and determining modes for the 3D Navier-Stokes-Voight equations
• Initial-boundary value problems for the equations of motion of Kelvin- Voigt fluids and Oldroyd fluids
• Nonlocal problems in the theory of equations of motion of Kelvin-Voigt fluids. II
• Nonlocal problems for the equations of motion of Kelvin-Voigt fluids
• Nonlocal problems in the theory of the motion equations of Kelvin-Voigt fluids
• Nonlocal problems for the equations of Kelvin-Voigt fluids and their \(\varepsilon\)-approximations in classes of smooth functions
• On the cost of controlling unstable systems: The case of boundary controls
• Navier-Stokes equation with hereditary viscosity
• Navier-Stokes-Voigt equations with memory in 3D lacking instantaneous kinematic viscosity
• Towards a theory of global solvability on \([0,\infty)\) for initial-boundary value problems for the equations of motion of Oldroyd and Kelvin-Voigt fluids
• Theory of nonstationary flows of Kelvin-Voigt fluids
• The study of initial-boundary value problems for mathematical models of the motion of Kelvin-Voigt fluids
• Pull-back attractors for three-dimensional Navier—Stokes—Voigt equations in some unbounded domains
• A Navier-Stokes-Voight model with memory
• Asymptotic behaviour of two–dimensional Navier–Stokes equations with delays
• Exact controllability of Galerkin’s approximations of micropolar fluids
• On NAVIER-STOKES and KELVIN-VOIGT Equations in Three Dimensions in Interpolation Spaces
• Contrôlabilité exacte des approximations de Galerkin des équations de Navier-Stokes
• ON THE POSITIVITY OF RIEMANN–STIELTJES INTEGRALS
• On the two-dimensional tidal dynamics system: stationary solution and stability
• Stabilization of Kelvin–Voigt viscoelastic fluid flow model
• Nonlinear Differential Equations of Monotone Types in Banach Spaces
• Flow invariance preserving feedback controllers for the Navier-Stokes equation.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the three dimensional Kelvin-Voigt fluids: global solvability, exponential stability and exact controllability of Galerkin approximations