磁流体方程组弱解在负指标Besov空间中基于旋度和电流的正则性标准

摘要

In this paper, the regularity criterion of weak solutions to the incompressible magneto-hydrodynamic equations is studied. Let (u(t, x), b(t, x)) be smooth solutions in (O, T), it is shown that the solution (u, b) can be extended beyond T provided that the vorticity and electric current (▽× u,▽× b) ∈ L 2/2-a (O, T;B-aa∞, ∞(R3)) ηL2/1-a(O,T;B-∞1,-a∞(R3)),0＜α＜1.Moreover this condition ensures that the solution is a smooth solution if it satisfies the energy inequality.%本文研究了不可压磁流体方程组弱解的正则性准则,设(u(t,x),6(t,x))是不可压磁流体方程组在(O,T)上的光滑解,如果旋度和电流密度满足(▽× u,▽× b) ∈ L 2-a/2 (O, T;B-aa∞, ∞(R3)) ηL1-a/2(O,T;B-∞1,-a∞(R3)),0＜α＜1,则光滑解(u(t,x),b(t,x))可以连续延拓到(O,T'),T'＞T.而且这个条件可以保证满足能量不等式的弱解是(O,T)上的光滑解.