Cutoff Ergodicity Bounds in Wasserstein Distance for a Viscous Energy Shell Model with Lévy Noise

Abstract

This article establishes explicit non-asymptotic ergodic bounds in the renormalized Wasserstein–Kantorovich–Rubinstein (WKR) distance for a viscous energy shell lattice model of turbulence with random energy injection. The system under consideration is driven either by a Brownian motion, a symmetric \(\alpha \)-stable Lévy process, a stationary Gaussian or \(\alpha \)-stable Ornstein–Uhlenbeck process, or by a general Lévy process with second moments. The obtained non-asymptotic bounds establish asymptotically abrupt thermalization. The analysis is based on the explicit representation of the solution of the system in terms of convolutions of Bessel functions.