Blowup for the stochastic nonlinear Schrödinger equation with multiplicative noise

DOI10.1214/009117904000000964zbMath1068.35191arXivmath/0506595OpenAlexW3101306265MaRDI QIDQ1781176

Anne de Bouard, Arnaud Debussche

Publication date: 23 June 2005

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

Full work available at URL: https://arxiv.org/abs/math/0506595

zbMATH Keywords

blowupwhite noisesupercritical nonlinear Schrödinger equation

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes (60J60) 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 (43)

Stochastic nonlinear Schrödinger equations ⋮ Blow-up for the stochastic nonlinear Schrödinger equations with quadratic potential and additive noise ⋮ On a stochastic Hardy-Littlewood-Sobolev inequality with application to Strichartz estimates for a noisy dispersion ⋮ The nonlinear Schrödinger equation driven by jump processes ⋮ Wave energy self-trapping by self-focusing in large molecular structures: a damped stochastic discrete nonlinear Schrödinger equation model ⋮ Stochastic nonlinear Schrödinger equation with Brown-noise boundary conditions of mixed type ⋮ Stochastic nonlinear Schrödinger equations: no blow-up in the non-conservative case ⋮ Stochastic nonlinear Schrödinger equation on half-line with boundary noise ⋮ Scattering for stochastic nonlinear Schrödinger equations ⋮ Effective approximation for a nonlocal stochastic Schrödinger equation with oscillating potential ⋮ Long time behavior of stochastic NLS with a small multiplicative noise ⋮ Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations ⋮ A random Schrödinger equation with time-oscillating nonlinearity and linear dissipation/gain ⋮ Exit from a basin of attraction for stochastic weakly damped nonlinear Schrödinger equations ⋮ Blow-up for a stochastic model of chemotaxis driven by conservative noise on \(\mathbb{R}^2\) ⋮ On the well-posedness for stochastic fourth-order Schrödinger equations ⋮ Global solutions of aggregation equations and other flows with random diffusion ⋮ Multi-bubble Bourgain-Wang solutions to nonlinear Schrödinger equations ⋮ Stochastic nonlinear Schrödinger equations in the defocusing mass and energy critical cases ⋮ Optimal bilinear control of stochastic nonlinear Schrödinger equations: mass-(sub)critical case ⋮ Classical limit for a system of non-linear random Schrödinger equations ⋮ 1D quintic nonlinear Schrödinger equation with white noise dispersion ⋮ A note on stochastic Schrödinger equations with fractional multiplicative noise ⋮ Uniqueness and blow-up for a stochastic viscous dyadic model ⋮ Global solution and blow-up of the stochastic nonlinear Schrödinger system ⋮ Stochastic nonlinear Schrödinger equation on an upper-right quarter plane with Dirichlet random boundary ⋮ Global energy solutions to a stochastic Schrödinger-Poisson system with multiplicative noise in two dimensions ⋮ The Cauchy problem for the Hartree equations under random influences ⋮ The nonlinear stochastic Schrödinger equation via stochastic Strichartz estimates ⋮ Small noise asymptotic of the timing jitter in soliton transmission ⋮ The nonlinear Schrödinger equation with white noise dispersion ⋮ On the stochastic Strichartz estimates and the stochastic nonlinear Schrödinger equation on a compact Riemannian manifold ⋮ On the well-posedness for stochastic Schrödinger equations with quadratic potential ⋮ Stochastic nonlinear Schrödinger equations with linear multiplicative noise: rescaling approach ⋮ A nonlinear Schrödinger equation with fractional noise ⋮ Behavior of solutions to the 1D focusing stochastic nonlinear Schrödinger equation with spatially correlated noise ⋮ Stochastic Schrödinger equation with Dirichlet noise boundary conditions ⋮ Finite-time singularity of the stochastic harmonic map flow ⋮ A note on log-log blow up solutions for stochastic nonlinear Schrödinger equations ⋮ Uniform large deviations for the nonlinear Schrödinger equation with multiplicative noise ⋮ Numerical analysis of the nonlinear Schrödinger equation with white noise dispersion ⋮ Construction of minimal mass blow-up solutions to rough nonlinear Schrödinger equations ⋮ On uniqueness of multi-bubble blow-up solutions and multi-solitons to \(L^2\)-critical nonlinear Schrödinger equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dynamics of optical pulses in randomly birefringent fibers
• The nonlinear Schrödinger equation. Self-focusing and wave collapse
• A semi-discrete scheme for the stochastic nonlinear Schrödinger equation
• A stochastic nonlinear Schrödinger equation with multiplicative noise
• On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation
• Existence of strong solutions for Itô's stochastic equations via approximations
• On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
• Asymptotic Transmission of Solitons through Random Media
• On stochastic convolution in banach spaces and applications
• The Stochastic Nonlinear Schrödinger Equation inH¹
• White noise in the two-dimensional nonlinear schrödinger equation
• Numerical simulation of focusing stochastic nonlinear Schrödinger equations
• Stochastic Equations in Infinite Dimensions

This page was built for publication: Blowup for the stochastic nonlinear Schrödinger equation with multiplicative noise