A Note on the Regularity of Inviscid Shell Models of Turbulence

@inproceedings{Constantin2006ANO,
  title={A Note on the Regularity of Inviscid Shell Models of Turbulence},
  author={Peter Constantin and Boris Levant and Edriss S. Titi},
  year={2006}
}
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 the energy, provided that the components of the solution satisfy |un| ≤ Ck−1/3 n ( √ n log(n+1))−1, for some positive absolute constant C, which is the analogue of the Onsager’s conjecture… CONTINUE READING