论文标题
关于固定埃里克森 - 莱斯和MHD系统的弱解决方案的规律性的一些评论
Some remarks on the regularity of weak solutions for the stationary Ericksen-Leslie and MHD systems
论文作者
论文摘要
我们考虑流体动力学中两个相关性的椭圆耦合系统。这些系统构成了整个三维空间，它们考虑了外力的作用。第一个系统涉及简化的Ericksen-Leslie（SEL）系统，该系统描述了液晶流的动力学。第二个系统是时间无关的磁性磁动力学（MHD）方程。对于（SEL）系统，我们获得了一个新标准，以提高弱解决方案的规律性，前提是它们属于某些均匀的Morrey空间。作为双产品，我们还为固定的Navier-Stokes方程和非线性谐波图流程获得了一些新的规律性标准。该新的规律性标准也适用于（MHD）方程。此外，对于最后一个系统，我们能够使用Gevrey类来证明所有有限的能量弱解决方案都是分析功能，只要外部力属于某些Gevrey类。
We consider two elliptic coupled systems of relevance in the fluid dynamics. These systems are posed on the whole three-dimensional space and they consider the action of external forces. The first system deals with the simplified Ericksen-Leslie (SEL) system, which describes the dynamics of liquid crystal flows. The second system is the time-independent magneto-hydrodynamic (MHD) equations. For the (SEL) system, we obtain a new criterion to improve the regularity of weak solutions, provided that they belong to some homogeneous Morrey space. As a bi-product, we also obtain some new regularity criterion for the stationary Navier-Stokes equations and for a nonlinear harmonic map flow. This new regularity criterion also holds true for the (MHD) equations. Furthermore, for this last system we are able to use the Gevrey class to prove that all finite energy weak solutions are analytic functions, provided the external forces belong to some Gevrey class.
