Serrin-type regularity criteria for the 3D MHD equations via one velocity component and one magnetic component

In this paper, we consider the Cauchy problem to the 3D MHD equations. We show that the Serrin--type conditions imposed on one component of the velocity $u_{3}$ and one component of magnetic fields $b_{3}$ with $$ u_{3} \in L^{p_{0},1}(-1,0;L^{q_{0}}(B(2))),\ b_{3} \in L^{p_{1},1}(-1,0;L^{q_{1}}(B(2))), $$ $\frac{2}{p_{0}}+\frac{3}{q_{0}}=\frac{2}{p_{1}}+\frac{3}{q_{1}}=1$ and $3

Keywords:

• Mathematical physics
• Initial value problem
• Physics
• Weak solution
• Magnetic field
• magnetic components
• Type (model theory)
• Component (group theory)
• Energy (signal processing)
• Magnetohydrodynamics

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