Almost sure well-posedness for the periodic 3D quintic nonlinear Schr\"odinger equation below the energy space

TL;DR

This paper establishes that the periodic 3D quintic nonlinear Schrödinger equation is almost surely well-posed locally in time for initial data below the energy space, advancing understanding in supercritical regimes.

Contribution

It proves almost sure local well-posedness for the supercritical periodic 3D quintic NLS, below the critical Sobolev space, which was previously unresolved.

Findings

Almost sure local well-posedness below H^1

Extension of well-posedness theory to supercritical regimes

Advancement in understanding of nonlinear Schrödinger equations

Abstract

In this paper we prove an almost sure local well-posedness result for the periodic 3D quintic nonlinear Schr\"odinger equation in the supercritical regime, that is below the critical space $H^1(\mathbb T^3)$.