Global existence of a strong solution to the planar radiative magnetohydrodynamic equations in the half-line

Hu Cheng; Weizheng Li; Rong Zhang; Hu Cheng; Weizheng Li; Rong Zhang

doi:10.3934/cam.2026011

Communications in Analysis and Mechanics

2026, Volume 18, Issue 2: 273-295. doi: 10.3934/cam.2026011

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Global existence of a strong solution to the planar radiative magnetohydrodynamic equations in the half-line

1.
School of Mathematics and Computer Sciences, Nanchang University, Nanchang 330031, P. R. China
2.
Institute of Mathematics and Interdisciplinary Sciences, Nanchang University, Nanchang 330031, P. R. China

Received: 26 October 2025 Revised: 13 January 2026 Accepted: 13 January 2026 Published: 07 April 2026
35Q35, 76N10, 76W05

The initial-boundary value problem of the planar radiative magnetohydrodynamic equations in the half-line was studied. We considered the Neumann boundary condition on the transverse magnetic field which was initially introduced by Kazhikhov in 1987. For the density-dependent viscosity and the degenerate heat-conductivity, we obtained the uniform upper and lower bounds of the density and the temperature, thus the global existence of a strong solution with large initial data to the magnetohydrodynamic system in the half-line was established.
- radiative MHD,
- density-dependent viscosity,
- degenerate heat-conductivity,
- global strong solution,
- half-line,
- Neumann boundary condition
Citation: Hu Cheng, Weizheng Li, Rong Zhang. Global existence of a strong solution to the planar radiative magnetohydrodynamic equations in the half-line[J]. Communications in Analysis and Mechanics, 2026, 18(2): 273-295. doi: 10.3934/cam.2026011

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Abstract

The initial-boundary value problem of the planar radiative magnetohydrodynamic equations in the half-line was studied. We considered the Neumann boundary condition on the transverse magnetic field which was initially introduced by Kazhikhov in 1987. For the density-dependent viscosity and the degenerate heat-conductivity, we obtained the uniform upper and lower bounds of the density and the temperature, thus the global existence of a strong solution with large initial data to the magnetohydrodynamic system in the half-line was established.

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