Energy conservation for the weak solutions to the 3D compressible magnetohydrodynamic equations of viscous non-resistive fluids in a bounded domain. (December 2021)

• Record Type: Journal Article
• Authors: Wang, Xiong; Liu, Sili
• Is Part Of: Nonlinear analysis. Volume 62(2021)
• Publication Date: 2021-12
• Subjects: Compressible MHD equations -- Viscous non-resistive fluids -- Bounded domain -- Weak solutions -- Energy conservation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103359
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, inspired by the work of Chen–Liang–Wang–Xu (Chen et al., 2020) on compressible Navier–Stokes equations, we obtain the energy conservation for weak solutions of the compressible non-resistive magnetohydrodynamic flows in a bounded domain Ω ⊂ R 3 . To ensure the energy conservation, we need the same regularity conditions of density and velocity as in Chen et al. (2020), moreover, H ∈ L t 4 L x 4 and ∇ H ∈ L t p 1 L x q 1, where p 1 = 4 p 3 p − 4, q 1 = 4 q 3 q − 4 . Under these conditions, p 1 ∈ ( 4 3, 2 ], q 1 ∈ ( 4 3, 12 7 ] when p ≥ 4 and q ≥ 6 .