论文标题
3D可压缩粘性非抗性MHD系统的全球小型解决方案
Global small solutions to the 3D compressible viscous non-resistive MHD system
论文作者
论文摘要
对于3D可压缩的磁性水力动力（MHD）方程而没有磁扩散的平滑解决方案始终是一个极具挑战性的开放问题。目前，该3D MHD系统在整个空间$ \ Mathbb r^3 $或周期盒$ \ Mathbb t^3 $即使初始数据很小或附近的稳态解决方案，目前没有全球适应性或稳定性结果。本文介绍了在任何背景磁场附近的平滑解决方案的全球存在和稳定性结果。
Whether or not smooth solutions to the 3D compressible magnetohydrodynamic (MHD) equations without magnetic diffusion are always global in time remains an extremely challenging open problem. No global well-posedness or stability result is currently available for this 3D MHD system in the whole space $\mathbb R^3$ or the periodic box $\mathbb T^3$ even when the initial data is small or near a steady-state solution. This paper presents a global existence and stability result for smooth solutions to this 3D MHD system near any background magnetic field satisfying a Diophantine condition.
