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International Journal of Differential Equations
Volume 2018, Article ID 9867215, 11 pages
Research Article

Existence of Global Solutions for Nonlinear Magnetohydrodynamics with Finite Larmor Radius Corrections

Department of Mathematics, West Virginia University, Morgantown, WV, USA

Correspondence should be addressed to Harumi Hattori; ude.uvw@irottahh

Received 13 September 2017; Accepted 26 November 2017; Published 28 January 2018

Academic Editor: Elena Kaikina

Copyright © 2018 Fariha Elsrrawi and Harumi Hattori. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We discuss the existence of global solutions to the magnetohydrodynamics (MHD) equations, where the effects of finite Larmor radius corrections are taken into account. Unlike the usual MHD, the pressure is a tensor and it depends on not only the density but also the magnetic field. We show the existence of global solutions by the energy methods. Our techniques of proof are based on the existence of local solution by semigroups theory and a priori estimate.