Existence of invariant measures for the stochastic damped Schrödinger equation

DOI10.1007/s40072-016-0090-1zbMath1379.60066arXiv1605.02014OpenAlexW2962934754WikidataQ115375231 ScholiaQ115375231MaRDI QIDQ1685678

Igor Kukavica, Ibrahim Ekren, Mohammed Ziane

Publication date: 19 December 2017

Published in: Stochastic and Partial Differential Equations. Analysis and Computations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.02014

zbMATH Keywords

invariant measuretightnesswhite noiseasymptotic compactnesslong time behaviorstochastic Schrödinger equationFeller propertyergodic measureAldous criterion

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60)

Related Items (14)

Existence of invariant measures for some damped stochastic dispersive equations ⋮ Invariant measure of stochastic damped Ostrovsky equation driven by pure jump noise ⋮ Ergodicity for the randomly forced Navier-Stokes system in a two-dimensional unbounded domain ⋮ Existence of invariant measures for the stochastic damped Schrödinger equation ⋮ Global martingale and pathwise solutions and infinite regularity of invariant measures for a stochastic modified Swift–Hohenberg equation ⋮ Unique ergodicity for a class of stochastic hyperbolic equations with additive space-time white noise ⋮ Ergodic results for the stochastic nonlinear Schrödinger equation with large damping ⋮ Invariant measures for a stochastic nonlinear and damped 2D Schrödinger equation ⋮ Invariant sample measures and random Liouville type theorem for a nonautonomous stochastic \(p\)-Laplacian equation ⋮ Ergodicity of stochastic damped Ostrovsky equation driven by white noise ⋮ Analysis of time fractional and space nonlocal stochastic nonlinear Schrödinger equation driven by multiplicative white noise ⋮ Asymptotic behavior of stochastic Schrödinger lattice systems driven by nonlinear noise ⋮ Parareal Exponential $\theta$-Scheme for Longtime Simulation of Stochastic Schrödinger Equations with Weak Damping ⋮ Upper semi-continuity of random attractors and existence of invariant measures for nonlocal stochastic Swift–Hohenberg equation with multiplicative noise

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On unique ergodicity in nonlinear stochastic partial differential equations
• Uniform attractor for non-autonomous nonlinear Schrödinger equation
• Ergodicity for a weakly damped stochastic nonlinear Schrödinger equation
• Scalar conservation laws with stochastic forcing
• Dissipativity and invariant measures for stochastic Navier-Stokes equations
• The stochastic nonlinear damped wave equation
• Asymptotic smoothing effect for weakly damped forced Korteweg-de Vries equations
• Invariant measure for the stochastic Navier-Stokes equations in unbounded 2D domains
• Existence of invariant measures for the stochastic damped Schrödinger equation
• Existence of a finite-dimensional global attractor for a damped parametric nonlinear Schrödinger equation
• Asymptotic smoothing and the global attractor of a weakly damped KdV equation on the real line.
• Regularity of the attractor for a weakly damped nonlinear Schrödinger equation in \(\mathbb{R}^2\)
• Basic properties of nonlinear stochastic Schrödinger equations driven by Brownian motions
• Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing
• Global \(L_2\)-solutions of stochastic Navier-Stokes equations
• Unique ergodicity for fractionally dissipated, stochastically forced 2D Euler equations
• Invariant measures for stochastic nonlinear beam and wave equations
• Invariant measures for stochastic partial differential equations in unbounded domains
• An Introduction to 3D Stochastic Fluid Dynamics
• Regularity of the attractor for a weakly damped nonlinear schrödinger equation
• The Stochastic Nonlinear Schrödinger Equation inH¹
• Ergodicity for Infinite Dimensional Systems
• Existence and Regularity of Invariant Measures for the Three Dimensional Stochastic Primitive Equations
• Invariant measures for a stochastic nonlinear Schroedinger equation
• Ergodicity for the randomly forced 2D Navier-Stokes equations

This page was built for publication: Existence of invariant measures for the stochastic damped Schrödinger equation