摘要
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),b(t,x))是不可压磁流体方程组在(0,T)上的光滑解,如果旋度和电流密度满足(▽×u,▽×b)∈L^(2/2-α)(0,T;(?)_(∞,∞)^(-α)(R^3))∩L^(2/1-α)(0,T;(?)_(∞,∞)^(-1-α)(R^3)),0<α<1,则光滑解(u(t,x),b(t,x))可以连续延拓到(0,T′),T′>T.而且这个条件可以保证满足能量不等式的弱解是(0,T)上的光滑解.
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 （0, T）, it is shown that the solution （u, b） can be extended beyond T provided that the vorticity and electric current （△↓×u,△↓×b）∈Lz/2-a（0,T;B^-a∞,∞（R^3））for 0〈α〈1.Moreover, this condition ensures that the solution is a smooth solution if it satisfies the energy inequality.
出处
《数学进展》
CSCD
北大核心
2008年第4期451-458,共8页
Advances in Mathematics（China）
基金
China Postdoctoral Science Foundation(No.20060390530)
Natural Science Foundation of Henan Province(No.0611055500)
Science Foundation of the Education Department of Henan Province(No.200510460008).
关键词
磁流体方程组
弱解的正则性
负指标Besov空间
Magneto-hydrodynamical system
regularity of weak solutions
negative index Besovspaces
