具有温度相关系数的平面磁流体动力学方程的全局大解

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2019-10-21 DOI:10.1142/s0219891619500164

Yachun Li, Zhaoyang Shang

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引用次数: 6

摘要

当粘性、磁扩散和热导率取决于比体积[公式：见正文]和温度[公式：看正文]时，我们考虑粘性和导热理想多变气体的平面可压缩磁流体动力学（MHD）系统。由于技术原因，假设粘度系数、磁扩散和热导率与[公式：见正文]成比例，其中[公式：参见正文]是满足某些自然条件的非退化光滑函数。当给定一般的大初始数据并且指数[公式：见正文]足够小时，我们证明了初边值问题的全局实时经典解的存在性和唯一性。对于平面霍尔磁流体动力学方程也建立了类似的结果。

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Global large solutions to planar magnetohydrodynamics equations with temperature-dependent coefficients

We consider the planar compressible magnetohydrodynamics (MHD) system for a viscous and heat-conducting ideal polytropic gas, when the viscosity, magnetic diffusion and heat conductivity depend on the specific volume [Formula: see text] and the temperature [Formula: see text]. For technical reasons, the viscosity coefficients, magnetic diffusion and heat conductivity are assumed to be proportional to [Formula: see text] where [Formula: see text] is a non-degenerate and smooth function satisfying some natural conditions. We prove the existence and uniqueness of the global-in-time classical solution to the initial-boundary value problem when general large initial data are prescribed and the exponent [Formula: see text] is sufficiently small. A similar result is also established for planar Hall-MHD equations.

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来源期刊

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.