Analytical Study of Certain Magnetohydrodynamic-alpha Models
摘要
In this paper we present an analytical study of a subgrid scale turbulence model of the three-dimensional magnetohydrodynamic (MHD) equations, inspired by the Navier-Stokes-alpha (also known as the viscous Camassa-Holm equations or the Lagrangian-averaged Navier-Stokes-alpha model). Specifically, we show the global well-posedness and regularity of solutions of a certain MHD-alpha model (which is a particular case of the Lagrangian averaged magnetohydrodynamic-alpha model without enhancing the dissipation for the magnetic field). We also introduce other subgrid scale turbulence models, inspired by the Leray-alpha and the modified Leray-alpha models of turbulence. Finally, we discuss the relation of the MHD-alpha model to the MHD equations by proving a convergence theorem, that is, as the length scale alpha tends to zero, a subsequence of solutions of the MHD-alpha equations converges to a certain solution (a Leray-Hopf solution) of the three-dimensional MHD equations.
引用
@article{arxiv.math/0606603,
title = {Analytical Study of Certain Magnetohydrodynamic-alpha Models},
author = {Jasmine S. Linshiz and Edriss S. Titi},
journal= {arXiv preprint arXiv:math/0606603},
year = {2007}
}
备注
26 pages, no figures, will appear in Journal of Math Physics; corrected typos, updated references