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Some notes on a class of equations in inertial manifold

Authors
Publisher
Elsevier Ltd
Publication Date
Volume
15
Identifiers
DOI: 10.1016/j.proeng.2011.08.379
Keywords
  • Manifold
  • Mode
  • Analytic Semigroup
  • Resolvent Operator
Disciplines
  • Mathematics

Abstract

Abstract The inertial manifold of dissipative partial differential equations is discussed by constructing an invariable map from low-dimensional Fourier mode to high-dimensional Fourier mode. The method is applied to the two-dimensional N-S equations with periodic boundary conditions, which shows that the invariable map from low-dimensional mode to high-dimensional mode is an attractor of this kind of equation in fact, further points out the injective relation between the orthogonal projection and the attractor.

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