带有阻尼项的三维微极流方程组的整体适定性  

GlobalWell-Posedness of the 3D Micropolar Fluid Equations with Damping

作　　者：祖倩 马宗立 ZU Qian;MA Zongli(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2024年第2期15-19,共5页Journal of Anqing Normal University(Natural Science Edition)

基　　金：2021年稳定博士科研启动费(213001)。

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。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 classical 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 

分 类 号：O177.1[理学—数学]