Global stability for the compressible isentropic magnetohydrodynamic equations in 3D bounded domains with Navier-slip boundary conditions
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909849944588288 |
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| author | Liu, Yang Wu, Guochun Zhong, Xin |
| author_facet | Liu, Yang Wu, Guochun Zhong, Xin |
| contents | 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 $L^2$-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 $L^\infty$-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 $L^6$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19749 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global stability for the compressible isentropic magnetohydrodynamic equations in 3D bounded domains with Navier-slip boundary conditions Liu, Yang Wu, Guochun Zhong, Xin Analysis of PDEs 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 $L^2$-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 $L^\infty$-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 $L^6$-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. |
| title | Global stability for the compressible isentropic magnetohydrodynamic equations in 3D bounded domains with Navier-slip boundary conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.19749 |