带阻尼项三维新MHD方程弱解的存在性
The Existence of Weak Solutions for the New MHD Equations with Damping in the Three Dimensional Space
DOI: 10.12677/AAM.2022.116436, PDF,   
作者: 宋 悦：辽宁师范大学数学学院，辽宁 大连
关键词: 新MHD方程；阻尼项；弱解；New MHD Equations； Damping Term； Weak Solutions
摘要: 本文给出了带阻尼项的新MHD方程在三维空间中弱解的存在性。我们通过标准Galerkin近似方法、Hölder不等式、Gromwall不等式、Schwartz不等式等基本不等式以及Parseval等式、先验估计和Fourier变换等得到弱解的存在性。
Abstract: In this paper, we show the existence of weak solutions for the new MHD equations with damping in the three dimensional space. The existence of the weak solutions is proved by standard Galerkin approximation method, Hölder inequality, Gromwall inequality, Schwartz inequality and Parseval equality, prior estimation and Fourier transform.
文章引用：宋悦. 带阻尼项三维新MHD方程弱解的存在性[J]. 应用数学进展, 2022, 11(6): 4079-4087. https://doi.org/10.12677/AAM.2022.116436

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