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arXiv · 1612.05366

Almost sure local well-posedness for the supercritical quintic NLS

Justin T. Brereton
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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.

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Justin T. Brereton. 2016-12-16. Almost sure local well-posedness for the supercritical quintic NLS. https://doi.org/10.2140/tunis.2019.1.427

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