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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Received: 6 February 2001 / Revised version: 18 July 2001 / Published online: 13 May 2002
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de Bouard, A., Debussche, A. On the effect of a noise on the solutions of the focusing supercritical nonlinear Schrödinger equation. Probab Theory Relat Fields 123, 76–96 (2002). https://doi.org/10.1007/s004400100183
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DOI: https://doi.org/10.1007/s004400100183