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Blow-up for the stochastic nonlinear Schrodinger equation with multiplicative noise

Anne de Bouard·Arnaud Debussche
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Abstract

We study the influence of a multiplicative Gaussian noise, white in time and correlated in space, on the blow-up phenomenon in the supercritical nonlinear Schrodinger equation. We prove that any sufficiently regular and localized deterministic initial data gives rise to a solution which blows up in arbitrarily small time with a positive probability.

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Anne de Bouard, Arnaud Debussche. 2005-06-29. Blow-up for the stochastic nonlinear Schrodinger equation with multiplicative noise. https://doi.org/10.1214/009117904000000964

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