On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation |
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| Authors: | A de Bouard A Debussche |
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| Institution: | (1) CNRS et Université Paris-Sud, UMR 8628, Bat. 425, Université de Paris-Sud, 91405 Orsay, France, FR;(2) ENS de Cachan, Antenne de Bretagne, Campus de Ker Lann, Av. R. Schuman, 35170 Bruz, France. e-mail: arnaud.debussche@bretagne.ens-cachan.fr, FR |
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| Abstract: | We investigate the influence of a random perturbation of white noise type on the finite time blow up of solutions of a focusing supercritical nonlinear Schrödinger equation. We prove that, contrary to the deterministic case, any initial data gives birth to a solution which develops singularities. Moreover, the singularities appear immediately. We use a stochastic generalization of the variance identity and a control argument. |
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