Analytic Study of Shell Models of Turbulence

Peter Constantin, Boris Levant, Edriss S. Titi

Published 2005-11-09, updated 2006-07-04Version 2

In this paper we study analytically the viscous `sabra' shell model of energy turbulent cascade. We prove the global regularity of solutions and show that the shell model has finitely many asymptotic degrees of freedom, specifically: a finite dimensional global attractor and globally invariant inertial manifolds. Moreover, we establish the existence of exponentially decaying energy dissipation range for the sufficiently smooth forcing.