2025/05/26 by Yang Liu, Guochun Wu, Liu, Yang +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2505.19749
openalex publication_date 2025/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the global stability of large solutions to the compressible isentropic magnetohydrodynamic equations in a three-dimensional (3D) bounded domain with Navier-slip boundary conditions. It is shown that the solutions converge to an equilibrium state exponentially in the L2-norm provided the density is essentially uniform-in-time bounded from above. Moreover, we also obtain that the density and magnetic field converge to their equilibrium states exponentially in the L^∞-norm if additionally the initial density is bounded away from zero. These greatly improve the previous work in (J. Differential Equations 288 (2021), 1-39), where the authors considered the torus case and required the L6-norm of the magnetic field to be uniformly bounded as well as zero initial total momentum and an additional restriction 2μ>λ for the viscous coefficients. This paper provides the first global stability result for large strong solutions of compressible magnetohydrodynamic equations in 3D general bounded domains.