Optimal mass normalizability for Gibbs measure associated with NLS on the 2D disc

2022/04/20 by Xian, Tianhao
#35Q55 (Secondary) #60H40 (Primary) 60H30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2204.09561

Abstract

We prove the normalizability of Gibbs measure associated with radial focusing nonlinear Schrödinger equation (NLS) on the 2-dimensional disc \mathbbD, at critical mass threshold. The result completes the study of optimal mass normalizability on \mathbbD by Oh-Sosoe-Tolomeo (2021).

Related

• Focusing Gibbs measures with harmonic potential
• Statistical mechanics of the radial focusing nonlinear Schrödinger equation in general traps
• Gibbs measures as local equilibrium KMS states for focusing nonlinear Schrödinger equations
• Local limit of the focusing discrete NLS
• Invariant Gibbs dynamics for the nonlinear Schrödinger equations on the disc