三维Electro-Hydrodynamics方程组光滑解的延拓准则

Extension criterion for the 3D Electro-Hydrodynamics equations

研究了三维Electro-Hydrodynamics方程组局部光滑解的延拓准则,利用负指标Besov空间中的对数Sobolev不等式和Kato-Ponce交换子估计方法,在Besov空间中获得了只涉及速度场水平分量的最优延拓准则,改进和推广了已有关于Electro-Hydrodynamics方程组正则性准则的部分结论,是Electro-Hydrodynamics方程组正则性理论的有益补充。

This paper investigates the extension criteria for the local smooth solution of the three-dimensional Electro-Hydrodynamics equations.By using the logarithmic Sobolev inequality in the Besov spaces with negative indices and the well known commutator estimate due to Kato and Ponce,the optimal extension criteria involving only the horizontal component of the velocity field are obtained in the Besov space.This result improves and extends some known regularity criteria of the three-dimensional incompressible Electro-Hydrodynamics equations,which is a supplement to the regularity theory.