On global regularity of 2D generalized magnetohydrodynamic equations
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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 . https://doi.org/10.1016/j.jde.2013.02.016
Journal of Differential Equations
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