Probabilistic well-posedness and Gibbs measure evolution for the non linear Schrödinger equation on the two dimensional sphere

We present recent results on probabilistic well-posedness of the two dimensional NLS, posed on the sphere. These results deal with low regularity solutions. The construction of such solutions is beyond the scope of applicability of the deterministic methods of Burq-Gérard-Tzvetkov developed between 2000 and 2004.

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Publication Details

Journal
Journées Équations aux dérivées partielles
Published
2026-06-19
DOI
https://doi.org/10.5802/jedp.700
Primary Topic
Stochastic processes and financial applications
Type
article
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article

Probabilistic well-posedness and Gibbs measure evolution for the non linear Schrödinger equation on the two dimensional sphere

Chenmin Sun, Nicolas Camps, Nicolas Burq, Nikolay Tzvetkov
Journées Équations aux dérivées partielles
Stochastic processes and financial applications
article

Probabilistic well-posedness and Gibbs measure evolution for the non linear Schrödinger equation on the two dimensional sphere

Chenmin Sun, Nicolas Camps, Nicolas Burq, Nikolay Tzvetkov
article en

Abstract

We present recent results on probabilistic well-posedness of the two dimensional NLS, posed on the sphere. These results deal with low regularity solutions. The construction of such solutions is beyond the scope of applicability of the deterministic methods of Burq-Gérard-Tzvetkov developed between 2000 and 2004.

Journées Équations aux dérivées partielles
École Normale Supérieure de Lyon (FR), Centre National de la Recherche Scientifique (FR), Institut Universitaire de France (FR), Université Paris-Est Créteil (FR), Université Paris-Saclay (FR), Laboratoire de Mathématiques d'Orsay (FR), Laboratoire d’Analyse et de Mathématiques Appliquées (FR), Unité de Mathématiques Pures et Appliquées (FR), Institut de recherche mathématique de Rennes (FR), Université de Rennes (FR)
Openalex Percentile: Top 5%
Stochastic processes and financial applications
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Probabilistic well-posedness and Gibbs measure evolution for the non linear Schrödinger equation on the two dimensional sphere — Chenmin Sun, Nicolas Camps, et al. · Journées Équations aux dérivées partielles (2026) | TGRS Research Map | TGRS