Global \(L_2\)-solutions of stochastic Navier-Stokes equations

DOI10.1214/009117904000000630zbMath1098.60062arXivmath/0503597OpenAlexW1998319262MaRDI QIDQ2497211

Boris L. Rosovskii, Remigijus Mikulevičius

Publication date: 3 August 2006

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0503597

zbMATH Keywords

strong solutionsWiener chaospathwise uniquenessLeray solutionKraichnan's turbulence

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Stochastic analysis applied to problems in fluid mechanics (76M35) Navier-Stokes equations (35Q30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (only showing first 100 items - show all)

Stochastic Navier-Stokes variational inequalities with unilateral boundary conditions: probabilistic weak solvability ⋮ Large deviation principle for a class of stochastic hydrodynamical type systems driven by multiplicative Lévy noises ⋮ Uniform tail-ends estimates of the Navier-Stokes equations on unbounded channel-like domains ⋮ Stochastic Navier-Stokes equations for turbulent flows in critical spaces ⋮ Regularization by transport noises for 3D MHD equations ⋮ Stochastic inviscid Leray-\( \alpha\) model with transport noise: convergence rates and CLT ⋮ Intrusive and non-intrusive chaos approximation for a two-dimensional steady state Navier-Stokes system with random forcing ⋮ Well-posedness and large deviations for 2D stochastic Navier-Stokes equations with jumps ⋮ Large deviation principle for the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity ⋮ On the stochastic Euler-Poincaré equations driven by pseudo-differential/multiplicative noise ⋮ Stochastic optimal control of a evolutionary p-Laplace equation with multiplicative Lévy noise ⋮ Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system ⋮ Layer methods for stochastic Navier-Stokes equations using simplest characteristics ⋮ Well-posedness of stochastic second grade fluids ⋮ Backward uniqueness of stochastic parabolic like equations driven by Gaussian multiplicative noise ⋮ Error estimates of finite element methods for fractional stochastic Navier-Stokes equations ⋮ Global existence for the stochastic Navier-Stokes equations with small \(L^p\) data ⋮ STATIONARY WEAK SOLUTIONS FOR STOCHASTIC 3D NAVIER–STOKES EQUATIONS WITH LÉVY NOISE ⋮ Strong solutions for the stochastic Cahn-Hilliard-Navier-Stokes system ⋮ Measure valued solutions to the stochastic Euler equations in \(\mathbb R^d\) ⋮ Existence and uniqueness of martingale solutions to option pricing equations with noise ⋮ Large deviation principles for 2-D stochastic Navier-Stokes equations driven by Lévy processes ⋮ Well-posedness of stochastic 2D hydrodynamics type systems with multiplicative Lévy noises ⋮ Stochastic tamed 3D Navier-Stokes equations: existence, uniqueness and ergodicity ⋮ On distribution free Skorokhod-Malliavin calculus ⋮ Global strong solution to the three-dimensional stochastic incompressible magnetohydrodynamic equations ⋮ Verification theorems for stochastic optimal control problems in Hilbert spaces by means of a generalized Dynkin formula ⋮ Large deviations and averaging for stochastic tamed 3D Navier-Stokes equations with fast oscillations ⋮ The stochastic tamed MHD equations: existence, uniqueness and invariant measures ⋮ Ergodicity Results for the Stochastic Navier–Stokes Equations: An Introduction ⋮ On the zeroth law of turbulence for the stochastically forced Navier-Stokes equations ⋮ Local and global strong solution to the stochastic 3-D incompressible anisotropic Navier-Stokes equations ⋮ 3D tamed Navier-Stokes equations driven by multiplicative Lévy noise: existence, uniqueness and large deviations ⋮ Approximations of stochastic 3D tamed Navier-Stokes equations ⋮ Weak martingale solution of stochastic critical Oldroyd-B type models perturbed by pure jump noise ⋮ Stochastic constrained Navier-Stokes equations on \(\mathbb{T}^2\) ⋮ On the asymptotic behaviour and stochastic stabilization of second grade fluids ⋮ Volatility uncertainty quantification in a stochastic control problem applied to energy ⋮ Stochastic tamed Navier-Stokes equations on \(\mathbb{R}^3\): the existence and the uniqueness of solutions and the existence of an invariant measure ⋮ Variational principles for fluid dynamics on rough paths ⋮ Existence of martingale solutions and the incompressible limit for stochastic compressible flows on the whole space ⋮ Large deviations for 2-D stochastic Navier-Stokes equations driven by multiplicative \textit{Lévy} noises ⋮ Existence of invariant measures for the stochastic damped Schrödinger equation ⋮ On unbiased stochastic Navier-Stokes equations ⋮ Stochastic hydrodynamic-type evolution equations driven by Lévy noise in 3D unbounded domains -- abstract framework and applications ⋮ On the Navier-Stokes equation perturbed by rough transport noise ⋮ On the existence and uniqueness of solutions to stochastic three-dimensional Lagrangian averaged Navier–Stokes equations ⋮ Implications of Kunita-Itô-Wentzell formula for \(k\)-forms in stochastic fluid dynamics ⋮ Stochastic control of tidal dynamics equation with Lévy noise ⋮ Random Perturbations of Viscous, Compressible Fluids: Global Existence of Weak Solutions ⋮ Optimal relaxed control of stochastic hereditary evolution equations with Lévy noise ⋮ Exponential mixing properties of the stochastic tamed 3D Navier-Stokes equation with degenerate noise ⋮ Smooth solutions of non-linear stochastic partial differential equations driven by multiplicative noises ⋮ Global solutions for random vorticity equations perturbed by gradient dependent noise, in two and three dimensions ⋮ Moderate deviation principle for the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity ⋮ Fractional stochastic active scalar equations generalizing the multi-dimensional quasi-geostrophic \& 2D-Navier-Stokes equations: the general case ⋮ Analysis of time fractional and space nonlocal stochastic incompressible Navier-Stokes equation driven by white noise ⋮ Stochastic Navier-Stokes equations driven by Lévy noise in unbounded 3D domains ⋮ On signed measure valued solutions of stochastic evolution equations ⋮ Weak solutions to stochastic 3D Navier-Stokes-\(\alpha \) model of turbulence: \(\alpha \)-asymptotic behavior ⋮ Stochastic Navier-Stokes equations with Caputo derivative driven by fractional noises ⋮ Local existence of strong solutions to the stochastic Navier-Stokes equations with \(L^p\) data ⋮ Local and global existence of smooth solutions for the stochastic Euler equations with multiplicative noise ⋮ The Combined Incompressible Quasineutral Limit of the Stochastic Navier--Stokes--Poisson System ⋮ Stochastic Navier-Stokes equations with artificial compressibility in random durations ⋮ Weak solutions and invariant measures of stochastic Oldroyd-B type model driven by jump noise ⋮ Stochastic 3D tamed Navier-Stokes equations: existence, uniqueness and small time large deviation principles ⋮ Quasilinear parabolic stochastic evolution equations via maximal \(L^p\)-regularity ⋮ 2D backward stochastic Navier-Stokes equations with nonlinear forcing ⋮ Anomalous dissipation in a stochastic inviscid dyadic model ⋮ Martingale solutions for the three-dimensional stochastic nonhomogeneous incompressible Navier-Stokes equations driven by Lévy processes ⋮ Stochastic vorticity equation in \(\mathbb{R}^2\) with not regular noise ⋮ Three examples of Brownian flows on \(\mathbb{R}\) ⋮ Stochastic Navier-Stokes equations on a thin spherical domain ⋮ Total variation flow perturbed by gradient linear multiplicative noise ⋮ Exponential mixing for stochastic PDEs: the non-additive case ⋮ On a rough perturbation of the Navier-Stokes system and its vorticity formulation ⋮ Stochastic modelling in fluid dynamics: Itô versus Stratonovich ⋮ A note on stochastic Navier-Stokes equations with not regular multiplicative noise ⋮ Uniqueness for a stochastic inviscid dyadic model ⋮ Global existence of a weak solution to 3d stochastic Navier-Stokes equations in an exterior domain ⋮ Pathwise solutions of the 2-D stochastic primitive equations ⋮ DENSITY DEPENDENT STOCHASTIC NAVIER–STOKES EQUATIONS WITH NON-LIPSCHITZ RANDOM FORCING ⋮ Magnetohydrodynamic turbulent flows: existence results ⋮ Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier-Stokes equations ⋮ Global martingale solutions for a stochastic population cross-diffusion system ⋮ On the small time asymptotics of the two-dimensional stochastic Navier-Stokes equations ⋮ 2D Euler equations with Stratonovich transport noise as a large-scale stochastic model reduction ⋮ Analysis of a stochastic implicit interface model for an immersed elastic surface in a fluctuating fluid ⋮ Local martingale and pathwise solutions for an abstract fluids model ⋮ Global well-posedness of the stochastic generalized Kuramoto-Sivashinsky equation with multiplicative noise ⋮ Global solutions to random 3D vorticity equations for small initial data ⋮ High mode transport noise improves vorticity blow-up control in 3D Navier-Stokes equations ⋮ Continuity of cost functional and optimal feedback controls for the stochastic Navier Stokes equation in 2D ⋮ Random dynamical systems generated by stochastic Navier-Stokes equations on a rotating sphere ⋮ Well-posedness of the 3D stochastic primitive equations with multiplicative and transport noise ⋮ Nonlinear stochastic partial differential equations with singular diffusivity and gradient Stratonovich noise ⋮ Circulation and Energy Theorem Preserving Stochastic Fluids ⋮ Construction of weak solutions of a certain stochastic Navier–Stokes equation ⋮ Remarks on uniqueness and strong solutions to deterministic and stochastic differential equations

Cites Work

• Quantum probability for probabilists
• Stochastic equations in Hilbert space with application to Navier-Stokes equations in any dimension
• Dissipativity and invariant measures for stochastic Navier-Stokes equations
• Two-dimensional Navier-Stokes equations driven by a space-time white noise
• Integration of Brownian vector fields.
• Martingale and stationary solutions for stochastic Navier-Stokes equations
• Ergodicity of the 2-D Navier-Stokes equation under random perturbations
• Existence of strong solutions for Itô's stochastic equations via approximations
• Phase transition in the passive scalar advection
• On the uniqueness of solutions of stochastic differential equations. II
• On the uniqueness of solutions of stochastic differential equations
• The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals
• SOME MATHEMATICAL PROBLEMS OF STATISTICAL HYROMECHANICS
• STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AND TURBULENCE
• Linear Parabolic Stochastic PDE and Wiener Chaos
• Stochastic Navier--Stokes Equations for Turbulent Flows
• Partial regularity of suitable weak solutions of the navier-stokes equations
• On the Cauchy Problem for Stochastic Stokes Equations
• Small-Scale Structure of a Scalar Field Convected by Turbulence
• Stochastic Navier-Stokes equations
• On the existence of a solution to stochastic Navier-Stokes equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Global \(L_2\)-solutions of stochastic Navier-Stokes equations