粘性依赖于温度的MHD方程组整体经典解的正则性

尚朝阳, 任凯芳, 唐福全

数学学报 ›› 2021, Vol. 64 ›› Issue (1) : 1-40.

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数学学报 ›› 2021, Vol. 64 ›› Issue (1) : 1-40. DOI: 10.12386/A2021sxxb0001
论文

粘性依赖于温度的MHD方程组整体经典解的正则性

    尚朝阳1,2, 任凯芳2, 唐福全2
作者信息 +

Global Regularity of Classical Solutions to the Planar MHD Equations with Temperature-dependent Viscosity

    Zhao Yang SHANG1,2, Kai Fang REN2, Fu Quan TANG2
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文章历史 +

摘要

本文主要研究可压缩非等熵平面磁流体动力学方程组的Cauchy问题整体经典解的正则性，其中方程组的粘性系数λ，μ，磁扩散系数η和热传导系数κ都是比容v和温度θ的函数，正比于h（v）θα，h是满足一定条件的非退化光滑函数.在正则性准则∫0 +∞||b||L∞2ds <+∞的条件下，当α适当小时，我们证明了大初值整体经典解的存在性.

Abstract

We study the global regularity of classical solutions to the Cauchy problem of planar magnetohydrodynamics equations when the viscosity coefficients λ, μ, magnetic diffusion coefficient η and the heat conductivity coefficient κ depend on the specific volume v and the temperature θ which are proportional to h(v)θα for certain non-degenerate smooth function h. Under the condition of regularity criterion ∫0 +∞||b||L∞2ds < +∞, when α is small, we prove the existence of global classical solution with large initial data.

关键词

MHD方程组 / 粘性依赖于温度 / 正则性准则 / 整体经典解

Key words

MHD equations / temperature-dependent viscosity / regularity criterion / global classical solutions

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尚朝阳, 任凯芳, 唐福全. 粘性依赖于温度的MHD方程组整体经典解的正则性. 数学学报, 2021, 64(1): 1-40 https://doi.org/10.12386/A2021sxxb0001
Zhao Yang SHANG, Kai Fang REN, Fu Quan TANG. Global Regularity of Classical Solutions to the Planar MHD Equations with Temperature-dependent Viscosity. Acta Mathematica Sinica, Chinese Series, 2021, 64(1): 1-40 https://doi.org/10.12386/A2021sxxb0001

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基金

国家自然科学基金资助项目（11571232，11831011）
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