Existence of solutions of the equations of electron magnetohydrodynamics in a bounded domain

Pages: 1019 - 1034, Volume 26, Issue 3, March 2010

doi:10.3934/dcds.2010.26.1019       Abstract        Full Text (212.9K)       Related Articles

Manuel Núñez - Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid, Spain (email)

Abstract: Electron magnetohydrodynamics (EMHD) models the flow of electrons in fast time scales in an inhomogeneous plasma, by considering the ions as stationary. A number of numerical studies has shown an interesting phenomenology, but so far no proof exists of existence of solutions for the main equation. This equation is similar to the vorticity equation of inviscid flows, but the techniques used to prove local existence in that case do not work well in a bounded domain. However, the formulation of the Cauchy solution for certain transport equations plus a number of estimates on the Hölder norm of the flux of a vector field are enough to provide a proof of existence of solutions in a certain time interval.

Keywords:  Electron magnetohydrodynamics, Hölder spaces, Schauder fixed point theorem.
Mathematics Subject Classification:  Primary: 35L70, 35Q35; Secondary: 76W05.

Received: June 2009;      Revised: October 2009;      Published: December 2009.