Work

Gibbs Dynamics for Fractional Nonlinear Schrödinger Equations with Weak Dispersion

Year: 2024

Type: article

Abstract: We consider the Cauchy problem for the one-dimensional periodic cubic nonlinear fractional Schrödinger equation (FNLS) with initial data distributed via its associated Gibbs measure. We construct global strong solutions with the flow property for the FNLS on the support of the Gibbs measure in the full dispersive range, thus resolving a question proposed by Sun and Tzvetkov (Nonlinear Anal 213, paper no. 112530, 2021). As a byproduct, we prove the invariance of the Gibbs measure and almost sure global well-posedness for FNLS.

Source: Communications in Mathematical Physics

DOI: 10.1007/s00220-024-05116-1

Authors: Rui Liang, Yuzhao Wang

Institutions: South China Normal University, University of Birmingham

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,890

Funder: Engineering and Physical Sciences Research Council