发表机构
Graduate School of Science, Nagoya City University; School of Mathematical Sciences, Anhui University（名古屋市立大学理学研究科; 安徽大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对三维带科里奥利力的不可压缩磁流体力学方程组柯西问题，利用精细色散估计得到速度场和磁场的精细衰减率，显著改进了Kim 2022年的相关研究结果。
AI 中文摘要
本文研究三维全空间中带科里奥利力的不可压缩磁流体力学方程组的柯西问题。对于大初值，当旋转速度足够快时，已知该柯西问题在临界索伯列夫空间$\boldsymbol{\text{H}}^{1/2}(\boldsymbol{\text{R}}^3)$中存在唯一全局解。通过运用精细的色散估计，本文得到了速度场和磁场的精细衰减估计，这些衰减率显著改进了Kim在2022年《J. Differential Equations》中于亚临界索伯列夫框架$\boldsymbol{\text{H}}^s(\boldsymbol{\text{R}}^3)$（$1/2<s<3/2$）下得到的结果。
英文摘要
In this paper, we consider the Cauchy problem for the incompressible magnetohydrodynamic equations with the Coriolis force in the three-dimensional whole space. For large initial data, it is known that the Cauchy problem admits a unique global solution in critical Sobolev space $\dot{H}^{1/2}(\mathbb{R}^3)$ provided that the speed of rotation is fast enough. By using delicate dispersive estimates, we show refined decay estimates of the velocity field and magnetic field. These decay rates significantly improve the ones obtained by Kim [\emph{J. Differential Equations.}, 2022] in the subcritical Sobolev framework $H^s(\mathbb{R}^3)$ with $1/2<s<3/2$.
