Global attractor for the time discretized modified three-dimensional BĂ©nard systems

  • Chaosheng Zhu, Southwest University, School of Mathematics and Statistics, Chongqing, 400715, P. R. China,


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
DOI: 10.18514/MMN.2021.3161

Download: MMN-3161