On the regularity of generalized MHD equations

This paper studies the regularity of generalized magneto-hydrodynamics equation on the condition 0 < α = β < 3 / 2 . It will show if ∇ u ∈ L p , q on [ 0 , T ) with 2 α p + 3 q ⩽ 2 α , 3 2 α < q ⩽ + ∞ , then the solution can be extended past T.