dorsal/arxiv
View SchemaA Note on the Regularity of Inviscid Shell Model of Turbulence
| Authors | Peter Constantin, Boris Levant, Edriss S. Titi |
|---|---|
| Categories | |
| ArXiv ID | physics/0607060 |
| URL | https://arxiv.org/abs/physics/0607060 |
| DOI | 10.1103/PhysRevE.75.016304 |
Abstract
In this paper we continue the analytical study of the sabra shell model of energy turbulent cascade initiated in \cite{CLT05}. 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 $|{u_n}| \le C k_n^{-1/3} (\sqrt{n} \log(n+1))^{-1}$, for some positive absolute constant $C$, which is the analogue 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.
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"abstract": "In this paper we continue the analytical study of the sabra shell model of\nenergy turbulent cascade initiated in \\cite{CLT05}. We prove the global\nexistence of weak solutions of the inviscid sabra shell model, and show that\nthese solutions are unique for some short interval of time. In addition, we\nprove that the solutions conserve the energy, provided that the components of\nthe solution satisfy $|{u_n}| \\le C k_n^{-1/3} (\\sqrt{n} \\log(n+1))^{-1}$, for\nsome positive absolute constant $C$, which is the analogue of the Onsager\u0027s\nconjecture for the Euler\u0027s equations. Moreover, we give a Beal-Kato-Majda type\ncriterion for the blow-up of solutions of the inviscid sabra shell model and\nshow the global regularity of the solutions in the ``two-dimensional\u0027\u0027\nparameters regime.",
"arxiv_id": "physics/0607060",
"authors": [
"Peter Constantin",
"Boris Levant",
"Edriss S. Titi"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1103/PhysRevE.75.016304",
"title": "A Note on the Regularity of Inviscid Shell Model of Turbulence",
"url": "https://arxiv.org/abs/physics/0607060"
},
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