Regularity of inviscid shell models of turbulence

In this paper we continue the analytical study of the sabra shell model of energy turbulent cascade. We prove the global existence of weak solutions of the inviscid sabra shell model, and show that these solutions are unique for some short interval of time. In addition, we prove that the solutions c...

Full description

Saved in:
Bibliographic Details
Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 75; no. 1 Pt 2; p. 016304
Main Authors Constantin, Peter, Levant, Boris, Titi, Edriss S
Format Journal Article
LanguageEnglish
Published United States 01.01.2007
Online AccessGet more information

Cover

More Information
Summary:In this paper we continue the analytical study of the sabra shell model of energy turbulent cascade. We prove the global existence of weak solutions of the inviscid sabra shell model, and show that these solutions are unique for some short interval of time. In addition, we prove that the solutions conserve energy, provided that the components of the solution satisfy /u(n)/ <or= Ck(n)(-1/3)[square root of n log(n+1)](-1) for some positive absolute constant C, which is the analog of the Onsager's conjecture for the Euler's equations. Moreover, we give a Beal-Kato-Majda type criterion for the blow-up of solutions of the inviscid sabra shell model and show the global regularity of the solutions in the "two-dimensional" parameters regime.
ISSN:1539-3755
DOI:10.1103/PhysRevE.75.016304