论文信息 - On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation

On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation

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.

A. Debussche | A. Debussche | A. de Bouard | A. de Bouard | A. Bouard

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