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Remark on the local well-posedness for NLS with the modulated dispersion

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arxiv 2407.20005 v1 pith:VT7JZGY5 submitted 2024-07-29 math.AP

Tomoyuki Tanaka This is my paper
classification math.AP
keywords chouk-gubinellidispersionlocalmodulatedresultwell-posednessadaptcauchy
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We consider the Cauchy problem of the nonlinear Schr\"odinger equation with the modulated dispersion and power type nonlinearities in any spatial dimensions. We adapt the Young integral theory developed by Chouk-Gubinelli [K. Chouk and M, Gubinelli, Comm. Partial Differential Equations 40 (2015)] and multilinear estimates which are based on divisor counting, and show the local well-posedness. Our result generalizes the result by Chouk-Gubinelli.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Nonlinear PDEs with modulated dispersion III: multiplicative noises

    math.AP 2026-07 accept novelty 7.0 of 10

    Irregular modulation of dispersion yields pathwise regularization-by-noise for multiplicative Young noise on stochastic KdV, giving local well-posedness in every Hs.

  2. Refined global well-posedness for the periodic modulated Korteweg-de Vries equation

    math.AP 2026-07 accept novelty 6.5 of 10

    With a sufficiently irregular modulation, the periodic modulated KdV is globally well-posed in H^s(T) for every real s, via a non-classical scaling that bypasses the s = -3/2 barrier.

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