GLOBAL ATTRACTOR FOR THE TIME DISCRETIZED MODIFIED THREE-DIMENSIONAL BE´NARD SYSTEMS

In this paper, we aim to study the existence of global attractors for the time discretized modified three-dimensional (3D) Benard systems. Using the backward implicit Euler scheme, we obtain the time discretization systems of 3D Benard systems. Then, by the Galerkin method and the Brouwer fixed poin...

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Published inMathematical notes (Miskolci Egyetem (Hungary)) Vol. 22; no. 1; pp. 457 - 483
Main Author Zhu, Chaosheng
Format Journal Article
LanguageEnglish
Published Miskolc University of Miskolc 01.01.2021
Subjects
Discretization
Existence theorems
Fixed points (mathematics)
Galerkin method
Inequality
Mechanics
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Summary:In this paper, we aim to study the existence of global attractors for the time discretized modified three-dimensional (3D) Benard systems. Using the backward implicit Euler scheme, we obtain the time discretization systems of 3D Benard systems. Then, by the Galerkin method and the Brouwer fixed point theorem, we prove the existence of the solution to this time-discretized systems. On this basis, we proved the existence of the attractor by the compact embedding theorem of Sobolev. Finally, we discuss the limiting behavior of the solution as N tends to infinity.
ISSN:1787-2405
1787-2413
DOI:10.18514/MMN.2021.3161