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Invariant Gibbs measures for 1D NLS in a trap by Dinh, Van Duong; Rougerie, Nicolas is a scholarly article available to read on EtoBox.

What is Invariant Gibbs measures for 1D NLS in a trap about?

We consider the one dimensional cubic nonlinear Schr{\"o}dinger 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.

Author

Dinh, Van Duong; Rougerie, Nicolas

Published

2023

Language

EN