三维不可压缩磁流体力学方程组自相似的Leray弱解的整体存在性

Global Existence of Self-Similar Leray Weak Solution For Three Dimensional Incompressible Magnetohydrodynamics Equations

研究了三维不可压缩磁流体力学方程组的Cauchy问题.利用在近初始时刻局部空间的正则性估计以及Leray-Schauder不动点定理,证明了当(-1)齐次初值光滑且满足伸缩不变性时,该Cauchy问题存在自相似的光滑Leray弱解.

This paper deals with the Cauchy problem of the three dimensional incompressible magnetohydrodynamics equations.Using the regularity estimation of the local space near the initial time and the Leray-Schauder fixed point theorem,the global existence of a smooth self-similar Leray weak solution to the Cauchy problem with the smooth and scaleinvariant initial data is achieved.