Global well-posedness and asymptotic behavior of 3D full compressible MHD equations with density-dependent viscosity and vacuum

• Published in: Zeitschrift für angewandte Mathematik und Physik Vol. 76; no. 5
• Main Author: Zhang, Mingyu
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.10.2025
• Subjects: Asymptotic properties; Boundary conditions; Compressibility; Decay rate; Density; Viscosity; Well posed problems
• ISSN: 0044-2275; 1420-9039
• DOI: 10.1007/s00033-025-02591-x

In this paper, the global well-posedness and asymptotic behavior are justified for the three-dimensional full compressible magnetohydrodynamic system with density-dependent viscosity and vacuum in a bounded domains subject to non-slip boundary condition for velocity, homogeneous Dirichlet boundary condition for temperature, and perfectly conducting boundary condition for magnetic field. Both the global existence and exponential decay rates of strong solutions are obtained. It is worth noting that for p∈(3,6), the estimate of ‖∇ρ‖Lp remains uniformly bounded for all t⩾0, which is in sharp contrast to that in (Li et al. in Global existence of classical solutions to full compressible Navier–Stokes equations with large oscillations and vacuum in 3D bounded domains, 2022. https://arxiv.org/abs/2207.00441), where the exponential growth of ‖∇ρ‖Lp was explored.