三维不可压缩N-S方程的一个对称约化及其精确解  

Symmetry Reduction and Solution to the Three-Dimensional Incompressible Navier-Stokes Equations

作　　者：夏浪[1] 

机构地区：[1]复旦大学力学与工程科学系,上海200433

出　　处：《力学季刊》2011年第4期525-530,共6页Chinese Quarterly of Mechanics

摘　　要：Lie对称方法在一定的条件下研究微分方程的群不变解和对称约化使得求解方程更为简洁,为研究偏微分方程的提供了有力的工具。本文运用Stokes-Helmholtz分解将三维不可压缩N-S方程转化为标量方程,再用Lie对称方法计算其相应的对称群,最后给出了标量方程的对称群以及相似解,并借此给出了N-S方程的精确解。Lie symmetry methods,which are proposed to study the invariant solutions of differential equations under specify conditions and symmetry reductions,simplify the process of solving the differential equations.Stokes-Helmholtz decomposition theorem was first applied to transform Navier-Stokes equation into a scalar partial differential equation;then,Lie symmetry method was employed to obtain the symmetry groups of the scalar partial differential equation.An analytic solution and its similarity solutions were also proposed.

关 键 词：对称群 N-S方程 偏微分方程 

分 类 号：O351.3[理学—流体力学] O152.5[理学—力学]