| 不可压磁流体方程在柱坐标下的表示及其基本能量估计 |
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| 引用本文： | 钟建新,赖祥威.不可压磁流体方程在柱坐标下的表示及其基本能量估计[J].宜春学院学报,2020(3):37-39,103. |
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| 作者姓名： | 钟建新 赖祥威 |
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| 作者单位： | 宜春学院应用数学研究中心;昆明理工大学理学院 |
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| 基金项目： | 江西省教育厅科技项目(项目编号:GJJ170891)。 |
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| 摘 要： | 在考虑方程解的适定性时,解有有限能量总是一个最基本要求。因此,对方程做基本能量估计是非常有必要的,也是考虑解的适定性的前提。本文给出了磁流体力学方程在柱对称条件下的解的基本能量估计,这为后续的解的存在唯一性,正则性等,提供了一个保障。首先运用微积分的知识,将直角坐标系下的梯度算子和拉普拉斯算子换算成柱坐标系下的情形,进而求得柱坐标系下的磁流体力学方程表达式,而后求该方程在无旋情形(所有变量关于角变量是固定的)的基本能量估计。
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| 关 键 词： | 磁流体方程 柱对称 基本能量估计 不可压方程 |
Representation of Incompressible MHD Equation in Cylindrical Coordinates and Its Basic Energy Estimation |
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| ZHONG Jian-xin,LAI Xiang-wei.Representation of Incompressible MHD Equation in Cylindrical Coordinates and Its Basic Energy Estimation[J].Journal of Yichun University,2020(3):37-39,103. |
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| Authors: | ZHONG Jian-xin LAI Xiang-wei |
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| Institution: | (Center of Applied Mathematics,Yichun University,Yichun 336000,China;School of Science,Kunming University of Science and Technology,Kunming 650500,China) |
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| Abstract: | It is well-known that finite energy is always a basic requirement when considering the existence of the solution.Therefore,it is very necessary to give the basic energy estimation of the solutions,and it is also a prerequisite to consider the existence of the solution.In this paper,we give the basic estimates to the MHD equations under cylindrical symmetry,which provides a guarantee for the existence,uniqueness and regularity of solutions.Firstly,the gradient operator and Laplacian operator are converted into the case in cylindrical coordinate system by calculus,and then the expression of MHD equations in cylindrical coordinate system is obtained.Sceondly,the energy estimation of MHD equations in irrotational case is obtained. |
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| Keywords: | MHD equations cylindrical symmetry basic energy estimation incomperssible equation |
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