Communications in Mathematical Sciences

Volume 10 (2012)

Number 2

Ladder theorem and length-scale estimates for a Leray alpha model of turbulence

Pages: 477 – 491



Hani Ali (IRMAR, Université Rennes 1, Rennes, France)


In this paper, we study the Modified Leray alpha model with periodic boundary conditions. We show that the regular solution satisfies a sequence of energy inequalities which are called “ladder inequalities”. Furthermore, we estimate some quantities of physical relevance in terms of the Reynolds number.


turbulence models, regularity, Navier-Stokes equations

2010 Mathematics Subject Classification

35Q30, 76B03, 76D05, 76F05

Published 21 December 2011