Dynamic Programming for the stochastic Navier-Stokes equations

DOI10.1051/m2an:2000151zbMath0953.76016OpenAlexW2015691753MaRDI QIDQ4950938

Arnaud Debussche, Giuseppe Da Prato

Publication date: 27 April 2000

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/197463

zbMATH Keywords

Hamilton-Jacobi-Bellman equationexistencedynamic programminguniquenesssmooth solutionstochastic Navier-Stokes equationoptimal cost problem

Mathematics Subject Classification ID

Dynamic programming in optimal control and differential games (49L20) Navier-Stokes equations for incompressible viscous fluids (76D05) Existence theories for optimal control problems involving partial differential equations (49J20) Statistical solutions of Navier-Stokes and related equations (76D06)

Related Items (13)

On the existence of optimal and \(\epsilon\)-optimal feedback controls for stochastic second grade fluids ⋮ The Kolmogorov operator associated to a Burgers SPDE in spaces of continuous functions ⋮ Optimal control for two-dimensional stochastic second grade fluids ⋮ Second order parabolic Hamilton-Jacobi-Bellman equations in Hilbert spaces and stochastic control: \(L^{2}_{\mu}\) approach ⋮ Ergodicity Results for the Stochastic Navier–Stokes Equations: An Introduction ⋮ Optimal control of path-dependent McKean-Vlasov SDEs in infinite-dimension ⋮ Optimal control for 3D stochastic Navier–Stokes equations ⋮ A stochastic maximum principle for control problems constrained by the stochastic Navier-Stokes equations ⋮ Mild solutions of semilinear elliptic equations in Hilbert spaces ⋮ Derivative formula for the Feynman-Kac semigroup of SDEs driven by rotationally invariant \(\alpha\)-stable process ⋮ On the dynamic programming approach for the 3D Navier-Stokes equations ⋮ Finite-horizon parameterizing manifolds, and applications to suboptimal control of nonlinear parabolic PDEs ⋮ Stochastic steady-state Navier-Stokes equations with additive random noise

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