Title :

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

Author(s) :

Dumont, Serge [Auteur]
Université de Nîmes [UNIMES]
Institut Montpelliérain Alexander Grothendieck [IMAG]
Goubet, Olivier [Auteur]
Systèmes de particules et systèmes dynamiques [Paradyse]
Mammeri, Youcef [Auteur]
Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 UPJV [LAMFA]

Journal title :

Discrete and Continuous Dynamical Systems - Series S

Pages :

2877-2891

Publisher :

American Institute of Mathematical Sciences

Publication date :

2021

ISSN :

1937-1632

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]

English abstract : [en]

In this article, the asymptotic behavior of the solution to the following one dimensional Schrodinger equations with white noise dispersionidu + u(xx) o dW + vertical bar u vertical bar(p-1)udt = 0 is studied. Here the ...
Show more >In this article, the asymptotic behavior of the solution to the following one dimensional Schrodinger equations with white noise dispersionidu + 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.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL