Regularity Condition For The Weak Solution Of The 3D MHD Equations Based On Partial Components

In this paper,we study regularity condition for the weak solution of the 3-dimensional incompressible MHD system in smooth bounded domains based on one component velocity and magnetic,namely v3 or ▽v3 and H.We use a general-ization of the Troisi inequality and anisotropic Lebesgue spaces and prove,that the condition v3∈Lβ(0,T;Lp),and p1,p2,p3 ∈(2,∞],3/4p1 + 3/4p2 + 1/P3<3/4,β∈(2,∞],p =(p1,p2,p3),the condition 2/β+1/p1+1/p2+1/p3=3/4+1/4p1+1/4p2 is right,the weak solution(v,H)of the incompressible 3D MHD equations with initial condition(v0,H0)∈ Wσ1,2 is regularity on(0,T]and we get another result,the relative index accord with under certain conditions,and if satisfies▽v3,▽H ∈ Lβ(0,T;Lp),the condition 2/β+∑i=13 1/pi=2-1/4q1-1/4q2 the weak solution(v,H)is regularity on(0,T].