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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).
|Pages (from-to)||44 - 67|
|Number of pages||24|
|Journal||Journal of the australian mathematical society|
|Early online date||21 Jun 2019|
|Publication status||Published - 31 Aug 2020|
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ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
1/03/15 → 29/02/20