Stochastic hydrodynamic-type evolution equations driven by Lévy noise in 3D unbounded domains -- abstract framework and applications

DOI10.1016/j.spa.2014.01.009zbMath1303.35075arXiv1306.5342OpenAlexW1983029909MaRDI QIDQ402401

Elżbieta Motyl

Publication date: 28 August 2014

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.5342

zbMATH Keywords

compactness methodembedding theoremsmartingale solutionLevy noise

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Stochastic analysis applied to problems in fluid mechanics (76M35) Navier-Stokes equations (35Q30) Magnetohydrodynamics and electrohydrodynamics (76W05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (32)

Well-posedness of stochastic 2D hydrodynamics type systems with multiplicative Lévy noises ⋮ Stochastic generalized magnetohydrodynamics equations with not regular multiplicative noise: well-posedness and invariant measure ⋮ Large deviation principles for a 2D stochastic Cahn–Hilliard–Navier–Stokes driven by jump noise ⋮ Stochastic magneto-hydrodynamic equations (MHD): invariant measures in 2D Poincaré domains ⋮ The stochastic tamed MHD equations: existence, uniqueness and invariant measures ⋮ Large deviation principles for a 2D stochastic Allen–Cahn–Navier–Stokes driven by jump noise ⋮ Weak martingale solution of stochastic critical Oldroyd-B type models perturbed by pure jump noise ⋮ Weak solution of a stochastic 2D Ericksen–Leslie model driven by jump noise ⋮ The Stampacchia maximum principle for stochastic partial differential equations forced by Lévy noise ⋮ Martingale solutions of the stochastic Hall-magnetohydrodynamics equations on \(\mathbb{R}^3\) ⋮ A stochastic Allen–Cahn–Navier–Stokes model with inertial effects driven by multiplicative noise of jump type ⋮ Existence and large time behavior for a stochastic model of modified magnetohydrodynamic equations ⋮ Stochastic control of tidal dynamics equation with Lévy noise ⋮ Central limit type theorem and large deviation principle for multi-scale McKean-Vlasov SDEs ⋮ Numerical ergodicity of two dimensional stochastic Navier-Stokes equations with Gaussian noise ⋮ Optimal relaxed control of stochastic hereditary evolution equations with Lévy noise ⋮ Well-posedness and large deviations for 2D stochastic Navier-Stokes equations with jumps ⋮ Weak solutions and invariant measures of stochastic Oldroyd-B type model driven by jump noise ⋮ Martingale solutions for the three-dimensional stochastic nonhomogeneous incompressible Navier-Stokes equations driven by Lévy processes ⋮ Time-splitting methods to solve the Hall-MHD systems with Lévy noises ⋮ Stochastic Navier-Stokes equations on a thin spherical domain ⋮ Weak and strong probabilistic solutions for a stochastic quasilinear parabolic equation with nonstandard growth ⋮ Weak solutions of a stochastic Landau-Lifshitz-Gilbert equation driven by pure jump noise ⋮ The exponential behavior and stabilizability of the stochastic magnetohydrodynamic equations ⋮ Weak solution of a stochastic 3D Cahn-Hilliard-Navier-Stokes model driven by jump noise ⋮ Ergodicity of Stochastic Shell Models Driven by Pure Jump Noise ⋮ On the weak solutions to a 3D stochastic Cahn-Hilliard-Navier-Stokes model ⋮ Fractionally Dissipative Stochastic Quasi-Geostrophic Type Equations on ${\mathbb{R}}^{d}$ ⋮ On the existence and uniqueness of solution to a stochastic simplified liquid crystal model ⋮ Stochastic generalized magnetohydrodynamics equations: well-posedness ⋮ Ergodicity of Stochastic Hydrodynamical-Type Evolution Equations Driven by $$\alpha $$-Stable Noise ⋮ Freidlin--Wentzell Type Large Deviation Principle for Multiscale Locally Monotone SPDEs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ergodicity of stochastic 2D Navier-Stokes equation with Lévy noise
• Martingale solutions and Markov selection of stochastic 3D Navier-Stokes equations with jump
• The Bénard problem with random perturbations: Dissipativity and invariant measures
• Stochastic tamed 3D Navier-Stokes equations: existence, uniqueness and ergodicity
• Maximal regularity for stochastic convolutions driven by Lévy processes
• Large deviations for stochastic tamed 3D Navier-Stokes equations
• Magnetohydrodynamic turbulent flows: existence results
• Existence of global solutions and invariant measures for stochastic differential equations driven by Poisson type noise with non-Lipschitz coefficients
• Large deviations for the Boussinesq equations under random influences
• Global solutions of stochastic 2D Navier-Stokes equations with Lévy noise
• Semimartingales: A course on stochastic processes
• Stochastic equations in Hilbert space with application to Navier-Stokes equations in any dimension
• Local existence and uniqueness of strong solutions to 3-D stochastic Navier-Stokes equations
• Martingale and stationary solutions for stochastic Navier-Stokes equations
• 2D stochastic Navier-Stokes equations driven by jump noise
• Existence of a martingale solution of the stochastic Navier-Stokes equations in unbounded 2D and 3D domains
• Martingale solutions for stochastic Navier-Stokes equations driven by Lévy noise
• Stochastic Navier-Stokes equations driven by Lévy noise in unbounded 3D domains
• Existence and ergodicity for the two-dimensional stochastic magneto-hydrodynamics equations
• Global \(L_2\)-solutions of stochastic Navier-Stokes equations
• Séminaire sur les fonctions aléatoires linéaires et les mesures cylindriques
• Equations stochastiques du type Navier-Stokes
• On the Fractal Dimension of Attractors for Viscous Incompressible Fluid Flows
• Some mathematical questions related to the mhd equations
• Lévy Processes and Stochastic Calculus
• Weak convergence of sequences of semimartingales with applications to multitype branching processes
• Attractors for the Bénard problem: existence and physical bounds on their fractal dimension
• The almost sure Skorokhod representation for subsequences in nonmetric spaces
• STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AND TURBULENCE
• Mathematical Problems of Statistical Hydromechanics
• THE STOCHASTIC MAGNETO-HYDRODYNAMIC SYSTEM
• Stochastic Navier--Stokes Equations for Turbulent Flows
• Stochastic Partial Differential Equations with Levy Noise
• On the existence of a solution to stochastic Navier-Stokes equations

This page was built for publication: Stochastic hydrodynamic-type evolution equations driven by Lévy noise in 3D unbounded domains -- abstract framework and applications