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arXiv · 2204.03280

Global dynamics of the $2d$ NLS with white noise potential and generic polynomial nonlinearity

N. Tzvetkov·N. Visciglia
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Abstract

Using an approach introduced by Hairer-Labb\' e we construct a unique global dynamics for the NLS on $\T^2$ with a white noise potential and an arbitrary polynomial nonlinearity. We build the solutions as a limit of classical solutions (up to a phase shift) of the same equation with smoothed potentials. This is an improvement on previous contributions of us and Debussche-Weber dealing with quartic nonlinearities and cubic nonlinearities respectively.

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N. Tzvetkov, N. Visciglia. 2022-04-07. Global dynamics of the $2d$ NLS with white noise potential and generic polynomial nonlinearity. https://doi.org/10.1007/s00220-023-04707-8

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