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

Abstract

We consider the Cauchy problem of the nonlinear Schrödinger 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.

13pages

References in corpus (4)

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• Almost sure well-posedness of the cubic nonlinear Schrödinger equation below L^2(T)
• Random data Cauchy theory for supercritical wave equations II : A global existence result
• On the wellposedness for periodic nonlinear Schrödinger equations with white noise dispersion