Internal Stabilization by Noise of the Navier–Stokes Equation

DOI10.1137/09077607XzbMath1215.35116OpenAlexW2017352803MaRDI QIDQ2999817

Viorel Barbu, Giuseppe Da Prato

Publication date: 17 May 2011

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/09077607x

zbMATH Keywords

Brownian motionstochastic processNavier-Stokes equationfeedback controller

Mathematics Subject Classification ID

Feedback control (93B52) Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Navier-Stokes equations (35Q30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Flow control and optimization for incompressible viscous fluids (76D55)

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Noise and stability in reaction-diffusion equations ⋮ Design of boundary stabilizers for the non-autonomous cubic semilinear heat equation driven by a multiplicative noise ⋮ Exponential stabilization of the linearized Navier-Stokes equation by pointwise feedback noise controllers ⋮ Global stabilization of the Navier-Stokes equations around an unstable steady state with mixed boundary kinetic energy controller ⋮ Control theory of stochastic distributed parameter systems: recent progress and open problems ⋮ Boundary stabilization of the Navier-Stokes equations with feedback controller via a Galerkin method ⋮ Exponential stabilization of the stochastic Burgers equation by boundary proportional feedback ⋮ Global solutions to random 3D vorticity equations for small initial data ⋮ Boundary stabilisation to non-stationary solutions for deterministic and stochastic parabolic-type equations ⋮ Global stabilization of the Navier-Stokes equations around an unstable equilibrium state with a boundary feedback controller

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