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Journal Articles Discrete and Continuous Dynamical Systems - Series S Year : 2021

Decay of solutions to one dimensional nonlinear Schrödinger equations with white noise dispersion

Abstract

In this article, the asymptotic behavior of the solution to the following one dimensional Schrodinger equations with white noise dispersion idu + u(xx) o dW + vertical bar u vertical bar(p-1)udt = 0 is studied. Here the equation is written in the Stratonovich formulation, and W (t) is a standard real valued Brownian motion. After establishing the global well-posedness, theoretical proof and numerical investigations are provided showing that, for a deterministic small enough initial data in L-x(1) boolean AND H-x(1), the expectation of the L-x(infinity) norm of the solutions decay to zero at O(t(-1/4)) as t goes to +infinity, as soon as p > 7.

Dates and versions

hal-02944262 , version 1 (21-09-2020)

Identifiers

Cite

Serge Dumont, Olivier Goubet, Youcef Mammeri. Decay of solutions to one dimensional nonlinear Schrödinger equations with white noise dispersion. Discrete and Continuous Dynamical Systems - Series S, 2021, 14 (8), pp.2877-2891. ⟨10.3934/dcdss.2020456⟩. ⟨hal-02944262⟩
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