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


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

published proceedings


author list (cited authors)

  • Linshiz, J. S., & Titi, E. S.

citation count

  • 64

complete list of authors

  • Linshiz, Jasmine S||Titi, Edriss S

publication date

  • June 2007