Work

Uniqueness of constraint minimizers for coupled planar Gross-Pitaevskii systems with logarithmic convolutions

Year: 2025

Type: article

Abstract: This paper is concerned with the $ L^2 $-critical minimization problem of the coupled planar Gross-Pitaevskii system with a harmonic potential and logarithmic convolutions. We first establish the existence and nonexistence of constraint minimizers for the system, which is connected with the unique positive solution of $ -\Delta u+u-u^3 = 0 $ in $ \mathbb{R}^2 $. The refined limiting behavior and exponential decay of nonnegative constraint minimizers are also analyzed. We further obtain the uniqueness of nonnegative constraint minimizers by overcoming the non-invariance under translations of the potential and the sign-changing property of the logarithmic convolutions.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2025136

Authors: Yujin Guo, Min Liu, Shu Zhang

Institutions: Central China Normal University, Liaoning Normal University, Xinyang Normal University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Central China Normal University

Awards: G5374449988, G7342254039