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JOURNALS // Theoretical and Applied Mechanics // Archive

Theor. Appl. Mech., 2024 Volume 51, Issue 2, Pages 165–188 (Mi tam147)

Global compact attractors and complete bounded trajectories for compressible magnetohydrodynamic system of equations

Jan Muhammad

Department of Mathematics, Shanghai University, Shanghai, P. R. China

Abstract: In this article, we investigate the global behavior of magnetohydrodynamic (MHD) fluid's weak solutions in three-dimensional bounded domain with a compact Lipschitz boundary driven by arbitrary forces. We show that global compact attractors exist under specific limitations on the adiabatic constant $\gamma$.

Keywords: weak solutions, compressible MHD fluid, bounded absorbing sets, asymptotic compactness, short trajectory, closed trajectory, attractor.

MSC: 76A05, 35Q35

Received: 28.08.2024
Accepted: 26.11.2024

Language: English

DOI: https://doi.org/10.2298/TAM240828009M



© Steklov Math. Inst. of RAS, 2025