We study by a combination of analytical and numerical Evans function techniques multi-D viscous and inviscid stability and associated transverse bifurcation of planar slow Lax MHD shocks in a channel with periodic boundary conditions. Notably, this includes the first multi-D numerical Evans function study for viscous MHD. Our results suggest that, rather than a planar shock, a nonplanar traveling wave with the same normal velocity is the typical mode of propagation in the slow Lax mode. Moreover, viscous and inviscid stability transitions appear to agree, answering (for this particular model and setting) an open question of Zumbrun and Serre.

我们通过分析和数值Evans函数技术的组合研究具有周期性边界条件的通道中平面慢Lax MHD冲击的多维粘性和无粘性稳定性以及相关的横向分叉。值得注意的是，这包括针对粘性MHD的首次多维Evans数值研究。我们的结果表明，慢速Lax模式下的典型传播模式不是平面冲击，而是具有相同法向速度的非平面行波。而且，粘性和无粘性的稳定过渡似乎是一致的，回答了（针对此特定模型和环境）Zumbrun和Serre的未解决问题。