论文标题
在具有分数拉普拉斯人的3D Hall-MHD方程式：全球适合
On 3D Hall-MHD equations with fractional Laplacians: global well-posedness
论文作者
论文摘要
研究了3D不可压缩的Hall-Magneto Hydroverantic（Hall-MHD）系统的问题，并研究了分数Laplacians的问题。首先，已证明了具有$ h^s $，$ s> \ frac {5} {2} $的一般初始数据的小能量解决方案的全局良好性。其次，构建了一类特殊的大能量初始数据，库奇问题在全球范围内都有良好的范围。证明依赖于涉及Littlewood-Paley分解和Sobolev不平等的新的全球能量估计，这使人们能够克服$ \ frac {1} {2} $ - 磁场的订单导数损失。
Cauchy problem for 3D incompressible Hall-magnetohydrodynamics (Hall-MHD) system with fractional Laplacians is studied. First, global well-posedness of small-energy solutions with general initial data in $H^s$, $s>\frac{5}{2}$, is proved. Second, a special class of large-energy initial data is constructed, with which the Cauchy problem is globally well-posed. The proofs rely upon a new global bound of energy estimates involving Littlewood-Paley decomposition and Sobolev inequalities, which enables one to overcome the $\frac{1}{2}$-order derivative loss of the magnetic field.
