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Blowup for the stochastic nonlinear Schrödinger equation with multiplicative noise. (English) Zbl 1068.35191

The authors study the influence of a multiplicative Gaussian noise, white in time and correlated in space, on the blowup phenomenon in the supercritical nonlinear Schrödinger equation. The authors 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.

MSC:

35R60 PDEs with randomness, stochastic partial differential equations
35Q55 NLS equations (nonlinear Schrödinger equations)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)
60J60 Diffusion processes
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