Linearization and normal form of the Navier-Stokes equations with potential forces(*)
Linearization and normal form of the Navier-Stokes equations with potential forces(*)
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DOI：
10.1016/s0294-1449(16)30372-9
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发表时间：
1987
影响因子：
1.9
通讯作者：
C. Foias;J. Saut
中科院分区：
文献类型：
--
作者：
C. Foias;J. Saut
借助于解的整体渐近展开式，我们导出了具有势(梯度)体力的Navier-Stokes方程的归一化理论。如果Stokes算符的谱没有共振，则范式是线性的Navier-Stokes系统。在一般情况下，规范形是在适当的Fréchet空间中的方程，其非线性项对应于共振。然而，它可以通过连续积分无穷序列的线性非齐次微分方程组来求解。归一化映射是全局定义的、解析的、一对一的。我们用两个简单的例子来说明我们的理论。特别地，我们将Burgers方程的正规化与Hopf-Cole变换联系起来。
We derive a normalization theory for the Navier-Stokes equations with potential (gradient) body forces by means of a global asymptotic expansion of a solution as time goes to infinity. The normal form is the linear Navier-Stokes system if the spectrum of the Stokes operator has no resonances. In the general case, the normal form is an equation in a suitable Fréchet space, whose nonlinear terms correspond to resonances. However, it can be solved by integrating successively an infinite sequence of linear nonhomogeneous differential equations. The normalization mapping is globally defined, analytic, one to one. We illustrate our theory by two simple examples. In particular we relate our normalization for the Burgers equation to the Hopf-Cole transform.