不可压霍尔磁流体力学方程组的全局解与衰减估计
Global Existence and Decay Estimates of Solutions for Incompressible Hall-Magnetohydrodynamics Systems
Abstract
研究三维不可压霍尔磁流体力学(Hall-MHD)方程组的柯西问题.通过纯能量方法得到了全局解的存在性及其最佳收敛率.特别地,还得到了解的高阶导数; 的最佳衰减率.证明基于纯能量方法和插值方法,没有像半群方法那样使用其线性化方程的衰减分析结果. We consider the Cauchy problem for incompressible; Hall-Magnetohydrodynamics (Hall-MHD) systems in; ${{\textbf{R}}^3}$.Global solutions and optimal convergence rates are; obtained by the pure energy method. In particular, optimal decay rates; of the higher-order spatial derivatives of solutions are obtained. Our; proof is based on a family of scaled energy estimates and interpolations; among them without the linear decay analysis as in a semigroup method.