Cutoff ergodicity bounds in Wasserstein distance for a viscous energy shell model with Lévy noise

Abstract

This article establishes non-asymptotic ergodic bounds in the renormalized, weighted Kantorovich-Wasserstein-Rubinstein distance for a viscous energy shell lattice model of turbulence with random energy injection. The obtained bounds turn out to be asymptotically sharp and establish abrupt thermalization. The types of noise under consideration are Gaussian and symmetric α-stable, white and stationary Ornstein-Uhlenbeck noise, respectively, as well as general Lévy noise with second moments. Furthermore we establish the absence of abrupt thermalization in the inviscid limit case.