The nonlinear Schrödinger equation with white noise dispersion
نویسنده
چکیده
Under certain scaling the nonlinear Schrödinger equation with random dispersion converges to the nonlinear Schrödinger equation with white noise dispersion. The aim of this work is to prove that this latter equation is globally well posed in L or H. The main ingredient is the generalization of the classical Strichartz estimates. Additionally, we justify rigorously the formal limit described above. March 19, 2010
منابع مشابه
1D quintic nonlinear Schrödinger equation with white noise dispersion
In this article, we improve the Strichartz estimates obtained in [12] for the Schrödinger equation with white noise dispersion in one dimension. This allows us to prove global well posedness when a quintic critical nonlinearity is added to the equation. We finally show that the white noise dispersion is the limit of smooth random dispersion.
متن کاملNonlinear Schrödinger Equation with a White-noise Potential: Phase-space Approach to Spread and Singularity
We propose a phase-space formulation for the nonlinear Schrödinger equation with a white-noise potential in order to shed light on two problems: the rate of dispersion and the singularity formation. Our main tools are the energy laws and the variance identity. The method is completely elementary. For the problem of dispersion, we show that in the absence of dissipation the ensemble-average disp...
متن کاملNumerical analysis of the nonlinear Schrödinger equation with white noise dispersion
This article is devoted to the numerical study of a nonlinear Schrödinger equation in which the coefficient in front of the group velocity dispersion is multiplied by a real valued Gaussian white noise. We first perform the numerical analysis of a semi-discrete Crank-Nicolson scheme in the case when the continuous equation possesses a unique global solution. We prove that the strong order of co...
متن کاملThe Schrödinger equation with spatial white noise potential
We consider the linear and nonlinear Schrödinger equation with a spatial white noise as a potential in dimension 2. We prove existence and uniqueness of solutions thanks to a change of unknown originally used in [8] and conserved quantities. 2010 Mathematics Subject Classification AMS:
متن کاملBlow-up for the Stochastic Nonlinear Schrödinger Equation with Multiplicative Noise
We study the influence of a multiplicative Gaussian noise, white in time and correlated in space, on the blow-up phenomenon in the supercritical nonlinear Schrödinger equation. We prove that any sufficiently regular and localized deterministic initial data gives rise to a solution which blows up in arbitrarily small time with a positive probability.
متن کامل