\(m\)-dissipativity of Kolmogorov operators corresponding to Burgers equations with space-time white noise

DOI10.1007/s11118-006-9021-5zbMath1119.35128OpenAlexW2054634226MaRDI QIDQ867114

Giuseppe Da Prato, Arnaud Debussche

Publication date: 14 February 2007

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11118-006-9021-5

zbMATH Keywords

smoothing propertiesfiniteness of moments\(m\)-dissipativitystochastic Burgers equationKolmogorpv equation

Mathematics Subject Classification ID

Nonlinear accretive operators, dissipative operators, etc. (47H06) KdV equations (Korteweg-de Vries equations) (35Q53) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items

The Kolmogorov operator associated to a Burgers SPDE in spaces of continuous functions ⋮ Moment estimates for invariant measures of stochastic Burgers equations ⋮ Coupling for some partial differential equations driven by white noise ⋮ Averaging principle for one dimensional stochastic Burgers equation ⋮ Random attractors for locally monotone stochastic partial differential equations ⋮ Gradient estimates and maximal dissipativity for the Kolmogorov operator in \(\Phi^4_2\) ⋮ Kolmogorov equation associated to a stochastic Kuramoto-Sivashinsky equation ⋮ Malliavin calculus for non-Gaussian differentiable measures and surface measures in Hilbert spaces ⋮ Gradient estimates for SDEs without monotonicity type conditions ⋮ Kolmogorov equations for randomly perturbed generalized Newtonian fluids ⋮ Improved moment estimates for invariant measures of semilinear diffusions in Hilbert spaces and applications ⋮ An integral inequality for the invariant measure of some finite dimensional stochastic differential equation ⋮ Derivative formula for the Feynman-Kac semigroup of SDEs driven by rotationally invariant \(\alpha\)-stable process ⋮ Fokker-Planck equation for Kolmogorov operators associated to stochastic PDE with multiplicative noise ⋮ Markovianity and ergodicity for a surface growth PDE ⋮ Kolmogorov operator and Fokker-Planck equation associated to a stochastic Burgers equation driven by Lévy noise ⋮ \(m\)-dissipativity for Kolmogorov operator of a fractional Burgers equation with space-time white noise

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dissipative operators in a Banach space
• Large deviations and the Malliavin calculus
• Ergodicity for the 3D stochastic Navier-Stokes equations
• Hausdorff dimension of a random invariant set
• Dirichlet forms and symmetric Markov processes
• The stochastic Burgers equation
• Attractors for random dynamical systems
• Differentiability of the Feynman-Kac semigroup and a control application
• Large deviations for a Burgers'-type SPDE
• A new approach to Kolmogorov equations in infinite dimensions and applications to stochastic generalized Burgers equations
• Weak solutions to stochastic porous media equations
• Existence and uniqueness results for semilinear stochastic partial differential equations
• The theory of generalized Dirichlet forms and its applications in analysis and stochastics
• THE STOCHASTIC BURGERS EQUATION: FINITE MOMENTS AND SMOOTHNESS OF THE DENSITY
• Stochastic burgers equation with correlated noise
• THE KOLMOGOROV EQUATION ASSOCIATED TO THE STOCHASTIC NAVIER–STOKES EQUATIONS IN 2D
• Stochastic Burgers' equation
• Stochastic Equations in Infinite Dimensions