论文标题
具有水平耗散和水平磁扩散的2D MHD方程的全局规律性
Global regularity for the 2D MHD equations with horizontal dissipation and horizontal magnetic diffusion
论文作者
论文摘要
本文建立了对2D MHD系统的经典解决方案的全局规律性，仅在剥离域中的水平耗散和水平磁扩散$ \ mathbb {t} \ times \ times \ mathbb {r} $当初始数据合适时。为了证明这一点，我们将Littlewood-Paley的分解与各向异性不平等相结合，以建立关键的换向器估计。我们还分析了溶液的渐近行为。另外，对于仅具有水平耗散的2D简化热带气候模型，获得了经典解决方案的全局存在和独特性。
This paper establishes the global regularity of classical solution to the 2D MHD system with only horizontal dissipation and horizontal magnetic diffusion in a strip domain $\mathbb{T}\times\mathbb{R}$ when the initial data is suitable small. To prove this, we combine the Littlewood-Paley decomposition with anisotropic inequalities to establish a crucial commutator estimate. We also analysis the asymptotic behavior of the solution. In addition, the global existence and uniqueness of classical solution is obtained for the 2D simplified tropical climate model with only horizontal dissipations.
