论文标题
通过空间平均重新审视的惯性歧管
Inertial manifolds via spatial averaging revisited
论文作者
论文摘要
本文对半连接抛物线方程的惯性流形进行了全面研究，并使用G. Sell和 J. Mallet-Paret。我们提出了一种通用方法，该方法涵盖了通过此方法获得的已知结果的大部分，并提供了许多新的结果。我们的应用中包括反应扩散方程，各种类型的广义Cahn-Hilliard方程，包括分数和第六阶Cahn-Hilliard方程以及几类改良的Navier-Stokes方程，包括Leray-$ leray-$α$正则化，过度鉴定的正则化及其组合。所有结果均在3D情况下获得周期性边界条件。
The paper gives a comprehensive study of inertial manifolds for semilinear parabolic equations and their smoothness using the spatial averaging method suggested by G. Sell and J. Mallet-Paret. We present a universal approach which covers the most part of known results obtained via this method as well as gives a number of new ones. Among our applications are reaction-diffusion equations, various types of generalized Cahn-Hilliard equations, including fractional and 6th order Cahn-Hilliard equations and several classes of modified Navier-Stokes equations including the Leray-$α$ regularization, hyperviscous regularization and their combinations. All of the results are obtained in 3D case with periodic boundary conditions.
