科研之友
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摘要
We present a regularity condition of a suitable weak solution to the MHD equations in three dimensional space with slip boundary conditions for a velocity and magnetic vector fields. More precisely, we prove a suitable weak solution are Holder continuous near boundary provided that the scaled mixed L-x,(t)p,(q)-norm of the velocity vector field with 3/p+2/q <= 2, 2 < q < infinity is sufficiently small near the boundary. Also, we will investigate that for this solution u is an element of L-x,(t)p,(q) with 1 <= 3/p + 2/q <= 3/2, 3 < p < infinity, the Hausdorff dimension of its singular set is no greater than max{p,q}(3/p + 2/q - 1).
- 出版日期2017-7
