| 田浩,吴菲,王泽军.具有双曲型热传导的可压缩 MHD 方程组解的衰减率[J].数学年刊A辑,2025,46(4):465~490 |
| 具有双曲型热传导的可压缩 MHD 方程组解的衰减率 |
| Decay Rates of the Compressible MHD Equations with Hyperbolic Heat Conduction |
| 投稿时间：2025-01-10 修订日期：2025-11-17 |
| DOI：10.16205/j.cnki.cama.2025.0029 |
| 中文关键词: 可压缩MHD方程组 Cattaneo热传导定律 全局存在性 大时间行为 最优时间衰减率 |
| 英文关键词:Compressible MHD equations Cattaneo’s heat conduction law Global existence Large-time behavior Optimal time-decay rates |
| 基金项目:江苏科技大学科学研究基金(No.1052932505) |
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| 中文摘要: |
| 研究了带有Cattaneo 热传导定律的非等熵可压缩 MHD方程组解的全局适定性和大时间行为. 与经典的 Fourier 热传导定律相比,Cattaneo 定律可以导出关于热流和温度的双曲型方程组,这意味着热量的传播速度有限, 更加符合自然规律. 在初始扰动小的假设下,该文严格建立了该系统经典解的全局存在性,并得到了解高阶空间导数的最优时间衰减率. 此外, 根据 Cattaneo定律中蕴含的阻尼结构可以推出, 与密度、速度、温度和磁场相比,热流具有更快的衰减率. |
| 英文摘要: |
| In this paper, the authors investigate the global well-posedness and large-time behavior of the compressible MHD equations with Cattaneo’s heat conduction law. Compared to the classical Fourier’s heat conduction law, Cattaneo’s law yields the hyperbolic equations governing heat flux and temperature. This implies that heat propagation occurs at a finite rate, aligning more closely with natural phenomena. Under the assumption of small initial perturbation, the authors rigorously establish the global existence of classical solution to the system and obtain the optimal time-decay rates of the higher-order spatial derivatives of the solution. Furthermore, the authors observe that the heat flux exhibits a faster time-decay rate compared to the density, velocity, temperature and magnetic field due to the damping structure in Cattaneo’s law. |
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