具有混合部分黏度的三维Hall-MHD系统光滑解的整体存在性

Pub Date : 2021-06-01 DOI:10.4208/jpde.v34.n1.1

Yuzhu Wang

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引用次数: 0

摘要

本文研究了具有混合部分黏度的三维广义Hall-MHD系统光滑解的整体存在性。混合部分黏度的扩散弱于全黏度，这给证明全局光滑解带来了新的困难。此外，霍尔项提高了标准MHD系统的非线性程度。在初始数据足够小的情况下，利用能量法和自举参数建立全局光滑解。AMS学科分类:76D03, 76W05中文图书馆分类:O175.29

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Global Existence of Smooth Solutions to Three Dimensional Hall-MHD System with Mixed Partial Viscosity

We investigate the global existence of smooth solutions to the three dimensional generalized Hall-MHD system with mixed partial viscosity in this work. The diffusion of mixed partial viscosity is weaker than that of full viscosity, which cases new difficulty in proving global smooth solutions. Moreover, Hall term heightens the level of nonlinearity of the standard MHD system. Global smooth solutions are established by using energy method and the bootstrapping argument, provided that the initial data is enough small. AMS Subject Classifications: 76D03, 76W05 Chinese Library Classifications: O175.29

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