理想磁流体动力学与场位错力学
Ideal Magnetohydrodynamics and Field Dislocation Mechanics
AI总结：
本文通过建立场位错力学与理想磁流体动力学的精确类比，利用补偿紧致性和凸积分方法转移弱解结果，并设计了对偶变分原理，为两类系统提供了统一分析框架。
摘要：
本文回顾了场位错力学的完全非线性（几何和材料）系统，以在适当的物理简化条件下建立其与理想磁流体动力学（理想MHD）方程的精确类比。近期，Faraco、Lindberg和Szekelyhidi利用Tartar和Murat的补偿紧致性方法以及凸积分技术，为理想MHD建立了具有各种守恒性质的弱解；通过已建立的类比，这些结果似乎可以转移到所考虑的场位错力学的理想化情形。本文为该偏微分方程组设计并讨论了一个对偶变分原理，该技术也可转移至MHD的研究中。
英文摘要：
The fully nonlinear (geometric and material) system of Field Dislocation Mechanics is reviewed to establish an exact analogy with the equations of ideal magnetohydrodynamics (ideal MHD) under suitable physically simplifying circumstances. Weak solutions with various conservation properties have been established for ideal MHD recently by Faraco, Lindberg, and Szekelyhidi using the techniques of compensated compactness of Tartar and Murat and convex integration; by the established analogy, these results would seem to be transferable to the idealization of Field Dislocation Mechanics considered. A dual variational principle is designed and discussed for this system of PDE, with the technique transferable to the study of MHD as well.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
