On global regularity of 2D generalized magnetohydrodynamic equations
MetadataShow full item record
In this article we study the global regularity of 2D generalized magnetohydrodynamic equations (2D GMHD), in which the dissipation terms are –ν(–Δ)αu and –κ(–Δ)βb. We show that smooth solutions are global in the following three cases: α≥1/2, β≥1; 0≤α≤1/2, 2α+β>2; α≥2, β=0. We also show that in the inviscid case ν=0, if β>1, then smooth solutions are global as long as the direction of the magnetic field remains smooth enough.
Tran , C V , Yu , X & Zhai , Z 2013 , ' On global regularity of 2D generalized magnetohydrodynamic equations ' Journal of Differential Equations , vol. 254 , no. 10 , pp. 4194-4216 . DOI: 10.1016/j.jde.2013.02.016
Journal of Differential Equations
This is an author version of this article. The published version Copyright © 2013 Elsevier Inc. is available from http://www.sciencedirect.com
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.