三维轴对称不可压Navier-Stokes方程的奇异性结构  

Singularity structure of incompressible three dimensional axi-symmetric Navier-Stokes equations

作　　者：邵曙光[1] 

机构地区：[1]北京工业大学应用数理学院,北京100124

出　　处：《南阳师范学院学报》2015年第12期1-6,共6页Journal of Nanyang Normal University

基　　金：河南省科技厅资助项目(132300410211;132300410440)

摘　　要：研究了三维轴对称不可压缩Navier-Stokes方程解u(x,t)的奇异性结构理论.利用直接微分方法,推导建立了柱坐标系下Navier-Stokes方程的完整表示形式.假设流体的速度在点(x_0,t_0)达到最大值Q_0=|u(x_0,t_0)|,或者r|u(x,t)在点(x_0,t_0)达到它的最大值r_0|u(x_0,t_0),并且对Q_0以及(x_0,t_0)作一个时空的尺度变换,则当r_0Q_0充分大时,在一个给定的抛物型区域中,解u(x,t)在C_(local)^(2,1,α)范数下趋向于一个非零的常向量.In this paper,the singularity structure theory of the incompressible three-dimensional axial symmetry Navier-Stokes equation is studied and the complete representation of the Navier-Stokes equation in the cylindrical coordinate system is derived through the direct differential method as well. If the flow speed reaches its maximum value Q0= ｜u（x0,t0）｜ at the point（x0,t0）,or if r｜u（x,t） reaches the maximum value r0｜u（x0,t0）｜ at the point（x0,t0）,and a transformation of the scale of the space and time with the factor Q0 and the center（x0,t0）is made,a tending to nonzero constant vector to Clocal^2,1,α norm with u（x,t） can be worked out in a fixed parabolic cube,provided that r0Q0 is sufficiently large.

关 键 词：NAVIER-STOKES方程 柱面坐标 轴对称 奇异性结构 

分 类 号：O29[理学—应用数学]