Periodic nonlinear Schrödinger equation with distributional potential and invariant measures

2024/05/01 by Arnaud Debussche, Debussche, Arnaud, Antoine Mouzard +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2405.00583

openalex publication_date 2024/05/01 · openalex created_date 2024/05/04 · openalex updated_date 2026/07/28

Abstract

In this paper, we continue some investigations on the periodic NLSE started by Lebowitz, Rose and Speer and by Bourgain with the addition of a distributional multiplicative potential. We prove that the equation is globally wellposed for a set of data of full normalized Gibbs measure, after suitable truncation in the focusing case. The set and the measure are invariant under the flow. The main ingredients used are Strichartz estimates on periodic NLS with distributional potential to obtain local well-posedness for low regularity initial data.

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