Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 29, pp. 1-10.

Title: Long-time behavior of solutions to the 2D magnetic B\'enard problem in porous media on unbounded domains

Author: Dang Thanh Son (Telecommunications Univ., Khanh Hoa, Vietnam)
  
Abstract:
In this article, we study the long time behavior of solutions to the 2D
magnetic Benard problem in porous media, considering on an arbitrary 
(bounded or unbounded) domain satisfying Poincare inequality. 
We first prove the existence of a weak solution and a global attractor 
for the problem. For $r=1,2,3$, we derive estimates for Hausdorff as well 
as fractal dimensions of the global attractors. We then show an upper 
semicontinuity of global attractors and final study the exponential 
stability of a stationary solution to the problem.

Submitted December 2, 2024. Published March 20, 2025.
Math Subject Classifications: 35B40, 35B41, 35Q35, 37L30, 76W05.
Key Words: Magnetic Benard problem; global attractor; porus medium
  fractal and Hausdroff dimensions; upper semicontinuity; stationary solution.