Sub and supercritical stochastic quasi-geostrophic equation

DOI10.1214/13-AOP887zbMath1322.60121arXiv1110.1984OpenAlexW1605523728MaRDI QIDQ2352753

Xiang Chan Zhu, Michael Roeckner, Rong-Chan Zhu

Publication date: 6 July 2015

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

Full work available at URL: https://arxiv.org/abs/1110.1984

zbMATH Keywords

well-posednessergodicitylaw of large numbersGaussian random fieldstrong Feller propertystochastic quasi-geostrophic equationMarkov selection

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Strong limit theorems (60F15) Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs in connection with geophysics (35Q86)

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Cites Work

• Unnamed Item
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• Central limit theorem for Markov processes with spectral gap in the Wasserstein metric
• Kolmogorov equations for stochastic PDEs.
• Ergodicity for a weakly damped stochastic nonlinear Schrödinger equation
• Existence and uniqueness of the solution to the dissipative 2D quasi-geostrophic equations in the Sobolev space
• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• 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
• Itô's formula in UMD Banach spaces and regularity of solutions of the Zakai equation
• Random attractors for a quasi-geostrophic dynamical system under stochastic forcing
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Itô's formula for the \(L _{p }\)-norm of stochastic \({W^{1}_{p}}\)-valued processes
• On ergodicity of some Markov processes
• Martingale solutions and Markov selections for stochastic partial differential equations
• Stopping times and tightness
• Dissipative quasi-geostrophic dynamics under random forcing
• Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics
• Coupling approach to white-forced nonlinear PDEs
• A maximum principle applied to quasi-geostrophic equations
• A coupling approach to randomly forced nonlinear PDE's. II
• Martingale and stationary solutions for stochastic Navier-Stokes equations
• Ergodicity of 2D Navier-Stokes equations with random forcing and large viscosity
• A concise course on stochastic partial differential equations
• Variation on a theme of Caffarelli and Vasseur
• The Yamada-Watanabe-Engelbert theorem for general stochastic equations and inequalities
• Exponential mixing for stochastic PDEs: the non-additive case
• Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing
• Markov selections for the 3D stochastic Navier-Stokes equations
• Global \(L_2\)-solutions of stochastic Navier-Stokes equations
• Markov solutions for the 3D stochastic Navier-Stokes equations with state dependent noise
• Ergodicity for the stochastic complex Ginzburg--Landau equations
• Exponential ergodicity for stochastic Burgers and 2D Navier-Stokes equations
• GLOBAL ATTRACTOR OF THE WEAKLY DAMPED WAVE EQUATION WITH NONLINEAR BOUNDARY CONDITIONS
• Brownian Representations of Cylindrical Local Martingales, Martingale Problem and Strong Markov Property of Weak Solutions of SPDEs in Banach Spaces
• Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
• On stochastic convolution in banach spaces and applications
• Behavior of Solutions of 2D Quasi-Geostrophic Equations
• Ergodicity for Infinite Dimensional Systems
• On the two dimensional quasi-geostrophic equations
• Uniqueness of the invariant measure for a stochastic PDE driven by degenerate noise
• A coupling approach to randomly forced nonlinear PDE's. I
• Stochastic Equations in Infinite Dimensions

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