Existence of densities for the 3D Navier-Stokes equations driven by Gaussian noise

DOI10.1007/s00440-013-0490-3zbMath1452.76193arXiv1203.0417OpenAlexW2010998506MaRDI QIDQ2447293

Arnaud Debussche, Marco Romito

Publication date: 25 April 2014

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.0417

zbMATH Keywords

Navier-Stokes equationsstochastic partial differential equationsBesov spacesdensity of laws

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Stochastic analysis applied to problems in fluid mechanics (76M35) Applications of stochastic analysis (to PDEs, etc.) (60H30) Navier-Stokes equations (35Q30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items

Solving a nonlinear fractional stochastic partial differential equation with fractional noise, Hölder regularity of the densities for the Navier-Stokes equations with noise, Absolute continuity of the solution to the stochastic Burgers equation, Density estimates for the solutions of backward stochastic differential equations driven by Gaussian processes, Existence of a density of the 2-dimensional stochastic Navier Stokes equation driven by Lévy processes or fractional Brownian motion, Existence of densities for multi-type continuous-state branching processes with immigration, A simple method for the existence of a density for stochastic evolutions with rough coefficients, Density analysis of non-Markovian BSDEs and applications to biology and finance, Compressible fluids driven by stochastic forcing: the relative energy inequality and applications, Time regularity of the densities for the Navier-Stokes equations with noise, On the anisotropic stable JCIR process, Non-elliptic SPDEs and Ambit Fields: Existence of Densities, Existence of densities for stochastic differential equations driven by Lévy processes with anisotropic jumps, Existence and Besov regularity of the density for a class of SDEs with Volterra noise, Finiteness of entropy for the homogeneous Boltzmann equation with measure initial condition

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Absolute continuity for some one-dimensional processes
• Ergodicity of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noise
• Theory of Bessel potentials. I
• Spatial smoothness of the stationary solutions of the 3D Navier-Stokes equations
• Ergodicity for the 3D stochastic Navier-Stokes equations
• Exponential mixing for the 3D stochastic Navier-Stokes equations
• Analysis of equilibrium states of Markov solutions to the 3D Navier-Stokes equations driven by additive noise
• Qualitative properties of stationary measures for three-dimensional Navier-Stokes equations
• Absolute continuity of the invariant measures for some stochastic PDEs
• Irreducibility of the 3-D stochastic Navier-Stokes equation
• Ergodicity of the finite-dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise
• Martingale and stationary solutions for stochastic Navier-Stokes equations
• Regularity of invariant measures for a class of perturbed Ornstein-Uhlenbeck operators
• Existence of densities for stable-like driven SDEs with Hölder continuous coefficients
• Finiteness of entropy for the homogeneous Boltzmann equation with measure initial condition
• Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noises
• Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing
• Markov selections for the 3D stochastic Navier-Stokes equations
• Markov selections and their regularity for the three-dimensional stochastic Navier-Stokes equations
• Markov solutions for the 3D stochastic Navier-Stokes equations with state dependent noise
• The small scales of the stochastic Navier-Stokes equations under rough forcing
• Partial regularity for the stochastic Navier-Stokes equations
• The Martingale Problem for Markov Solutions to the Navier-Stokes Equations
• An Introduction to 3D Stochastic Fluid Dynamics
• The Malliavin Calculus and Related Topics
• Malliavin calculus for the stochastic 2D Navier—Stokes equation
• Stochastic Equations in Infinite Dimensions