Article ID Journal Published Year Pages File Type
837967 Nonlinear Analysis: Real World Applications 2012 9 Pages PDF
Abstract

In this paper, we establish two new regularity criteria for the 3D incompressible MHD equations involving partial components of the velocity and magnetic fields. It is proved that if u3,b∈Lα(0,T;Lγ(R3)),2α+3γ≤34+12γ,γ>103 or u3,b∈Lα1(0,T;Lγ1(R3)),with2α1+3γ1≤1,3<γ1≤∞,∂3u1,∂3u2∈Lα2(0,T;Lγ2(R3)),with2α2+3γ2≤2,32<γ2≤∞, then the local strong solution (u,b)(u,b) remains smooth on [0,T][0,T].

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