MMN-3161
Global attractor for the time discretized modified three-dimensional Bénard systems
Chaosheng Zhu;Abstract
In this paper, we aim to study the existence of global attractors for the time discretized modified three-dimensional (3D) B\'{e}nard systems.Using the backward implicit Euler scheme, we obtain the time discretization systems of 3D B\'{e}nard 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.
Vol. 22 (2021), No. 1, pp. 457-483