Almost sure local well-posedness for the supercritical quintic NLS

Abstract

This paper studies the quintic nonlinear Schrödinger equation on ${\mathbb{R}}^d$ with randomized initial data below the critical regularity $H^{\frac{d-1}{2}}$. The main result is a proof of almost sure local well-posedness given a Wiener Randomization of the data in $H^s$ for $s\in (\frac{d-2}{2},\frac{d-1}{2})$. The argument further develops the techniques introduced in the work of Á. Bényi, T. Oh and O. Pocovnicu on the cubic problem. The paper concludes with a condition for almost sure global well-posedness.

21 pages

References in corpus (2)

• Random data Cauchy theory for supercritical wave equations I: Local theory
• Loss of regularity for supercritical nonlinear Schrodinger equations

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