Invariant Gibbs measures for 1D NLS in a trap

2023/01/06 by Dinh, Van Duong, Rougerie, Nicolas · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2301.02544

Abstract

We consider the one dimensional cubic nonlinear Schrödinger equation with trapping potential behaving like |x| s (s > 1) at infinity. We construct Gibbs measures associated to the equation and prove that the Cauchy problem is globally well-posed almost surely on their support. Consequently, the Gibbs measure is indeed invariant under the flow of the equation. We also address the construction and invariance of canonical Gibbs measures, conditioned on the L 2 mass.

Cited by

• Large deviation principles for the Gross Pitaevskii Gibbs measure at low temperature

Related

• Long time dynamics for the one dimensional non linear Schrödinger equation
• Invariant measure for the Schrödinger equation on the real line
• Invariant Gibbs measures for the one-dimensional quintic nonlinear Schrödinger equation in infinite volume
• Invariant Gibbs measures and global strong solutions for nonlinear Schrödinger equations in dimension two
• Invariant measure for the Klein-Gordon equation in a non periodic setting