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September  2010, 26(3): 1019-1034. doi: 10.3934/dcds.2010.26.1019

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

Manuel Núñez 1,

1. 

Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid, Spain

Received  June 2009 Revised  October 2009 Published  December 2009

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: 76W0.
Citation: Manuel Núñez. Existence of solutions of the equations of electron magnetohydrodynamics in a bounded domain. Discrete & Continuous Dynamical Systems, 2010, 26 (3) : 1019-1034. doi: 10.3934/dcds.2010.26.1019
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