Almost surely smoothed scattering for cubic NLS

Herbert Koch; Nicolas Burq; Nicola Visciglia; Nikolay Tzvetkov

Almost surely smoothed scattering for cubic NLS

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arxiv 2406.07713 v2 pith:BGXCX4ST submitted 2024-06-11 math.AP

Nicolas Burq , Herbert Koch , Nicola Visciglia , Nikolay Tzvetkov This is my paper · ORCID

classification math.AP

keywords almostcubicscatteringsurelyassociatedconsiderconvergencedata

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We consider cubic NLS in dimensions 2, 3, 4 and we prove that almost surely solutions with randomized initial data at low regularity scatter. Moreover, we establish some smoothing properties of the associated scattering operator and precise the rate of convergence.

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Exponential mixing for the randomly forced NLS equation
math.AP 2025-06 conditional novelty 7.0 of 10

Under localized damping and noise, the randomly forced NLS on the 1D torus admits a unique invariant measure and exponentially fast convergence in the dual-Lipschitz metric.

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