带有阻尼项的三维微极流方程组的整体适定性
Global Well-Posedness of the 3D Micropolar Fluid Equations with Damping
祖倩 1马宗立1
作者信息
- 1. 安庆师范大学 数理学院,安徽 安庆 246133
- 折叠
摘要
本文研究了在三维情形下带有阻尼项的不可压微极流方程组的整体适定性问题.在某些特定条件下,微极流方程组可以退化成经典的Navier-Stokes方程组,因此考虑将Navier-Stokes方程组的相关成果推广到微极流方程组.由于微极流方程组在速度场基础上考虑了微旋转速度场,其结构更加复杂.本文通过对微极流方程组的非线性结构细致分析和能量估计,得到了当1+3/β+1<α<min{5/2,2+3/β+1},β>1时方程组存在唯一的整体解.
Abstract
In this paper, the global well-posedness of the incompressible micropolar fluid equations with damping terms in three dimensions is studied. When subjected to a certain conditions, micropolar fluid equations can be reduced to the classi-cal Navier-Stokes equations. Therefore, this paper considers extending the relevant results of the Navier-Stokes equations to the equations of micropolar fluid equations. However, the structure of micropolar fluid equations is more complicated because the micropolar fluid equations consider the micro-rotational velocity field on the basis of the velocity field. By means of the detailed analysis of the structure of the model equations and combining with energy methods. We prove that there is a unique global solution of the equations for 1+3/β+1＜α＜min{5/2,2+3/β+1},β＞1.
关键词
微极流方程组/整体适定性/能量估计/阻尼Key words
micropolar fluid equations/global well-posedness/energy methods/damping引用本文复制引用
基金项目
2021年稳定博士科研启动费(213001)
出版年
2024
国家科技期刊平台
NSTL
万方数据