论文标题
通过各向异性线性操作员的直接正常模式方法，部分阻尼的2D MHD方程的全局适合度
Global well-posedness of the partially damped 2D MHD equations via a direct normal mode method for the anisotropic linear operator
论文作者
论文摘要
我们证明了2D不可压缩的非抗性MHD方程的全局良好性，其速度阻尼项附近是非零恒定背景磁场。为此，我们新设计了一种正常模式的方法，可以有效利用线性传播器的各向异性编码非耐药性MHD系统的部分耗散性质和基础磁场的稳定机制。通过基于Duhamel的表述，通过特征值分析以纠缠的方式隔离新密钥数量，并以纠缠的方式估算了它们，我们为任何初始数据$（v_0，b_0）$建立了全球适应性，在大于$ h^{4} \ cap l^1 $的空间中足够小。这改善了Siam J. Math的最新作品。肛门。 47，2630-2656（2015）获得相似的结果，但前提是$（v_0，b_0）$在严格嵌入$ h^{20} \ cap w^{6,1} $的空间中足够小。
We prove the global well-posedness of the 2D incompressible non-resistive MHD equations with a velocity damping term near the non-zero constant background magnetic field. To this end, we newly design a normal mode method of effectively leveraging the anisotropy of the linear propagator that encodes both the partially dissipative nature of the non-resistive MHD system and the stabilizing mechanism of the underlying magnetic field. Isolating new key quantities and estimating them with themselves in an entangling way via the eigenvalue analysis based on Duhamel's formulation, we establish the global well-posedness for any initial data $(v_0,B_0)$ that is sufficiently small in a space rougher than $H^{4}\cap L^1$. This improves the recent work in SIAM J. Math. Anal. 47, 2630-2656 (2015) where the similar result was obtained provided that $(v_0,B_0)$ was small enough in a space strictly embedded in $H^{20}\cap W^{6,1}$.
