INERTIAL MANIFOLDS AND SLOW MANIFOLDS

被引：11

作者：

DEBUSSCHE, A

TEMAM, R

机构：

[1] The Institute for Applied Mathematics, Scientific Computing Indiana University, Bloomington

[2] Laboritoire d'Analyse Numérique Université Paris-Sud, 91405 ORSAY CEDEX

来源：

APPLIED MATHEMATICS LETTERS | 1991年 / 4卷 / 04期

关键词：

D O I：

10.1016/0893-9659(91)90059-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The concept of slow manifold has been introduced in meteorology and is broadly used for short term weather forecast and data assimilation (see e.g., [1,2]). Our object in this article is to present a mathematical theory of slow manifolds, using the concept of inertial manifold recently studied in dynamical systems theory. We show in fact that a slow manifold is a special type of inertial manifold. Our study relies on a new construction of inertial manifolds for evolution equations of a more general type than those previously studied.

引用

页码：73 / 76

页数：4

共 13 条

[1]

Daley, Normal mode initialization, Rev. of Geoph. and Space Physics, 19, pp. 450-468, (1981)

[2]

Tribbia, Nonlinear Initialization on an Equatorial Beta-Plane, Monthly Weather Review, 105, pp. 704-713, (1979)

[3]

Tribbia, On Variational Normal Mode Initialization, Monthly Weather Review, 110, pp. 455-470, (1982)

[4]

Foias, Sell, Temam, Variétés inertielles des équations différentielles dissipatives, C.R. Acad. Sci. Paris, Série I, 301 t., pp. 139-142, (1985)

[5]

Foias, Sell, Temam, Inertial manifolds for nonlinear evolutionary equations, Journal of Differential Equations, 13, pp. 309-353, (1988)

[6]

Constantin, Foias, Nicolaenko, Temam, Nouveaux résultats sur les variétés inertielles pour les équations différentielles dissipatives, C.R. Acad. Sci. Paris, Série I, 302 t., pp. 375-378, (1986)

[7]

Constantin, Foias, Nicolaenko, Temam, Integral and inertial manifolds for dissipative partial differential equations, (1988)

[8]

Mallet-Paret, Sell, Inertial manifolds for reaction diffusion equations in higher space dimensions, Journal of the American Mathematical Society, 1, 4, pp. 805-866, (1988)

[9]

Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, (1988)

[10]

Leith, Nonlinear Normal Mode Initialization and Quasi-Geostrophic Theory, Journal of the Atmospheric Sciences, 37, pp. 955-958, (1980)

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