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Stochastic nonlinear Schrödinger equation with almost space-time white noise. (English) Zbl 1442.35418

Summary: We study the stochastic cubic nonlinear Schrödinger equation (SNLS) with an additive noise on the one-dimensional torus. In particular, we prove local well-posedness of the (renormalized) SNLS when the noise is almost space-time white noise. We also discuss a notion of criticality in this stochastic context, comparing the situation with the stochastic cubic heat equation (also known as the stochastic quantization equation).

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
60H30 Applications of stochastic analysis (to PDEs, etc.)
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