Probabilistic well-posedeness for the nonlinear Schrödinger equation on the 2d sphere I: positive regularities

2024/04/28 by Burq, Nicolas, Camps, Nicolas, Sun, Chenmin +1 · 2 citations
#35A01 #35Q55 #35R01 #35R60 #37KXX #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.18229

Abstract

We establish the probabilistic well-posedness of the nonlinear Schrödinger equation on the 2d sphere \mathbbS². The initial data are distributed according to Gaussian measures with typical regularity H^s(\mathbbS²), for s>0. This level of regularity goes significantly beyond existing deterministic results, in a regime where the flow map cannot be extended uniformly continuously.

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• Invariant Gibbs dynamics for the nonlinear Schrödinger equations on the disc
• Probabilistic well-posedness of dispersive PDEs beyond variance blowup I: Benjamin-Bona-Mahony equation

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