Scaling and saturation in infinite-dimensional control problems with applications to stochastic partial differential equations

DOI10.1007/s40818-018-0052-1zbMath1410.35118arXiv1706.01997OpenAlexW2963048334WikidataQ129117718 ScholiaQ129117718MaRDI QIDQ667932

Jonathan C. Mattingly, David P. Herzog, Nathan E. Glatt-Holtz

Publication date: 4 March 2019

Published in: Annals of PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.01997

zbMATH Keywords

Malliavin calculusfluid turbulencegeometric control theorystochastic partial differential equations (SPDEs)degenerate stochastic forcing and hypoellipticity

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) PDEs in connection with fluid mechanics (35Q35) Geometric methods (93B27) Stochastic calculus of variations and the Malliavin calculus (60H07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Hypoelliptic equations (35H10) Control of turbulent flows (76F70)

Related Items (9)

Almost-sure exponential mixing of passive scalars by the stochastic Navier-Stokes equations ⋮ Lagrangian chaos and scalar advection in stochastic fluid mechanics ⋮ Almost-sure enhanced dissipation and uniform-in-diffusivity exponential mixing for advection-diffusion by stochastic Navier-Stokes ⋮ Quantitative spectral gaps for hypoelliptic stochastic differential equations with small noise ⋮ Controllability and ergodicity of three dimensional primitive equations driven by a finite-dimensional force ⋮ Lower bounds on the Lyapunov exponents of stochastic differential equations ⋮ Approximate controllability of nonlinear parabolic PDEs in arbitrary space dimension ⋮ Large Prandtl number asymptotics in randomly forced turbulent convection ⋮ A regularity method for lower bounds on the Lyapunov exponent for stochastic differential equations

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