Analytical study of certain magnetohydrodynamic-α models Academic Article uri icon

abstract

  • 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- α (also known as the viscous Camassa-Holm equations or the Lagrangian-averaged Navier-Stokes- α model). Specifically, we show the global well-posedness and regularity of solutions of a certain MHD- α model (which is a particular case of the Lagrangian averaged magnetohydrodynamic- α model without enhancing the viscosity for the magnetic field). We also introduce other subgrid scale turbulence models, inspired by the Leray- α and the modified Leray- α models of turbulence. Finally, we discuss the relation of the MHD- α model to the MHD equations by proving a convergence theorem, that is, as the length scale α tends to zero, a subsequence of solutions of the MHD- α equations converges to a certain solution (a Leray-Hopf solution) of the three-dimensional MHD equations. © 2007 American Institute of Physics.

author list (cited authors)

  • Linshiz, J. S., & Titi, E. S.

citation count

  • 59

publication date

  • June 2007