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 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.
Constantin
Peter
P
Department of Mathematics, University of Chicago, Chicago, Illinois 60637, USA. const@math.uchicago.edu
Levant
Boris
B
Titi
Edriss S
ES