Invariant measures for a stochastic nonlinear and damped 2D Schrödinger equation

DOI10.1088/1361-6544/ad0f3azbMath1530.35273arXiv2106.07043OpenAlexW3168015197MaRDI QIDQ6181840

Margherita Zanella, Benedetta Ferrario, Zdzisław Brzeźniak

Publication date: 20 December 2023

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.07043

zbMATH Keywords

nonlinear Schrödinger equationinvariant measuretightnessGalerkin approximationpathwise uniquenessmultiplicative noisesequential weak Feller

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Applications of stochastic analysis (to PDEs, etc.) (60H30) NLS equations (nonlinear Schrödinger equations) (35Q55) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) PDEs on manifolds (35R01) PDEs with measure (35R06)

Cites Work

• Stochastic nonlinear Schrödinger equations
• Stochastic geometric wave equations with values in compact Riemannian homogeneous spaces
• On a class of martingale problems on Banach spaces
• A note on stochastic Navier-Stokes equations with not regular multiplicative noise
• Stochastic nonlinear Schrödinger equations with linear multiplicative noise: rescaling approach
• Ergodicity for a weakly damped stochastic nonlinear Schrödinger equation
• Itô's formula in UMD Banach spaces and regularity of solutions of the Zakai equation
• Applied functional analysis. Functional analysis, Sobolev spaces and elliptic differential equations
• Analysis of the Laplacian on a complete Riemannian manifold
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• Infinite-dimensional dynamical systems in mechanics and physics.
• Martingale solutions and invariant measures for stochastic evolution equations in Banach spaces
• Invariant measure for the stochastic Navier-Stokes equations in unbounded 2D domains
• Existence of invariant measures for the stochastic damped Schrödinger equation
• Stochastic vorticity equation in \(\mathbb{R}^2\) with not regular noise
• Stochastic nonlinear beam equations
• A stochastic nonlinear Schrödinger equation with multiplicative noise
• On sequentially weakly Feller solutions to SPDE's
• Applied functional analysis. Applications to mathematical physics. Vol. 1
• Existence of a martingale solution of the stochastic Navier-Stokes equations in unbounded 2D and 3D domains
• Stochastic Navier-Stokes equations driven by Lévy noise in unbounded 3D domains
• The nonlinear stochastic Schrödinger equation via stochastic Strichartz estimates
• Solution properties of a 3D stochastic Euler fluid equation
• The stochastic nonlinear Schrödinger equation in unbounded domains and non-compact manifolds
• Uniqueness of martingale solutions for the stochastic nonlinear Schrödinger equation on 3d compact manifolds
• Invariant measures for stochastic damped 2D Euler equations
• Existence of a unique solution and invariant measures for the stochastic Landau-Lifshitz-Bloch equation
• Weak martingale solutions for the stochastic nonlinear Schrödinger equation driven by pure jump noise
• Martingale solutions for the stochastic nonlinear Schrödinger equation in the energy space
• Invariant measures for stochastic nonlinear Schrödinger equations. Numerical approximations and symplectic structures
• On global existence and blow-up for damped stochastic nonlinear Schrödinger equation
• Stochastic nonlinear Schrödinger equations: no blow-up in the non-conservative case
• On the stochastic Strichartz estimates and the stochastic nonlinear Schrödinger equation on a compact Riemannian manifold
• Invariant measures for stochastic nonlinear beam and wave equations
• La théorie générale de la mesure dans son application à l'étude des systèmes dynamiques de la mécanique non linéaire
• Ergodic results for the stochastic nonlinear Schrödinger equation with large damping
• Regularity of spectral fractional Dirichlet and Neumann problems
• Weak Solutions to Stochastic Wave Equations with Values in Riemannian Manifolds
• Qualitative properties for the stochastic Navier-Stokes equation
• Brownian Representations of Cylindrical Local Martingales, Martingale Problem and Strong Markov Property of Weak Solutions of SPDEs in Banach Spaces
• A First Course in Sobolev Spaces
• Dispersive estimates with loss of derivatives via the heat semigroup and the wave operator
• The Stochastic Nonlinear Schrödinger Equation inH¹
• Uniqueness for stochastic evolution equations in Banach spaces
• Strichartz inequalities and the nonlinear Schrodinger equation on compact manifolds
• Ergodicity for Infinite Dimensional Systems
• Stationary solutions for stochastic damped Navier-Stokes equations in \mathBB{R}^d
• Spectral multiplier theorems of Hormander type on Hardy and Lebesgue spaces
• On Strichartz estimates for Schrödinger operators in compact manifolds with boundary
• Invariant measures for a stochastic nonlinear Schroedinger equation
• Stochastic Equations in Infinite Dimensions
• 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
• Unnamed Item

This page was built for publication: Invariant measures for a stochastic nonlinear and damped 2D Schrödinger equation