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<p>This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line. In particular, the transverse magnetic field is assumed to satisfy the Neumann boundary condition, which was first investigated by Kazhikhov in 1987. We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data. More precisely, our result can be regarded as a natural generalization of Kazhikov’s result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.</p>

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Global strong solutions to the planar compressible magnetohydrodynamic equations with degenerate heat-conductivity in the half-line

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Mengdi Tong,
  • Xue Wang,
  • Rong Zhang

摘要

This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line. In particular, the transverse magnetic field is assumed to satisfy the Neumann boundary condition, which was first investigated by Kazhikhov in 1987. We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data. More precisely, our result can be regarded as a natural generalization of Kazhikov’s result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.