Regularity Criterion of Weak Solutions to the 3D Incompressible Hall-magnetohydro dynamic Equations

摘要

In this paper, we study the regularity criterion of weak solutions to the 3D incompressible Hall-magnetohydrodynamics, which is if u and B satisfy the condition RT 0 k∂x3 u(t)kqLp +k∇BkγLβdt < ∞ with 3p + 2q ≤ 1, 3β + 2γ ≤ 1, p > 3, β > 3, then the weak solution (u, B) is a smooth one on (0, T ].