Unique local weak solutions of the non-resistive MHD equations in homogeneous Besov space

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Applicable Analysis Pub Date : 2023-10-12 DOI:10.1080/00036811.2023.2268634

Baoquan Yuan, Xueli Ke

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Abstract

ABSTRACTIn this paper, the local existence and uniqueness of weak solutions to a d-dimensional non-resistive MHD equations in homogeneous Besov spaces are studied. Specifically we obtain the local existence of a weak solution (u,b) of the non-resistive MHD equations for the initial data u0∈B˙p,1dp−1(Rd) and b0∈B˙p,1dp(Rd) with 1≤p≤∞, and the uniqueness of the weak solution when 1≤p≤2d. Compared with the previous results for the non-resistive MHD equations, in the local existence part, the range of p extends to 1≤p≤∞ from 1≤p≤2d, but the uniqueness of the solution requires 1≤p≤2d yet.KEYWORDS: Non-resistive MHD equationshomogeneous Besov spaceuniquenessweak solutionMATHEMATIC SUBJECT CLASSIFICATIONS (2000): 35Q3576D0376W05 Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementData sharing not applicable to this article as no datasets were generated or analysed during the current study.Additional informationFundingThe work of B. Yuan was partially supported by the Innovative Research Team of Henan Polytechnic University [grant number T2022-7], and double first-class discipline project [grant number AQ20230775].

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齐次Besov空间中非电阻MHD方程的唯一局部弱解

摘要本文研究了齐次Besov空间中d维非电阻MHD方程弱解的局部存在唯一性。具体地说，我们得到了初始数据u0∈b˙p,1dp−1(Rd)和b0∈b˙p,1dp(Rd)当1≤p≤∞时非电阻MHD方程弱解(u,b)的局部存在性，以及当1≤p≤2d时弱解的唯一性。与以往非电阻MHD方程的结果相比，在局部存在部分，p的范围由1≤p≤2d扩展到1≤p≤∞，但解的唯一性仍要求1≤p≤2d。关键词:非电阻MHD方程齐次Besov空间唯一性弱解数学学科分类(2000):35Q3576D0376W05披露声明作者未报告潜在利益冲突。数据可用性声明数据共享不适用于本文，因为在当前研究期间没有生成或分析数据集。袁b的工作得到了河南理工大学创新课题组[批准号:T2022-7]和双一流学科项目[批准号:AQ20230775]的部分资助。

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来源期刊

Applicable Analysis 数学-应用数学

CiteScore

2.60

自引率

9.10%

发文量

175

审稿时长

2 months

期刊介绍： Applicable Analysis is concerned primarily with analysis that has application to scientific and engineering problems. Papers should indicate clearly an application of the mathematics involved. On the other hand, papers that are primarily concerned with modeling rather than analysis are outside the scope of the journal General areas of analysis that are welcomed contain the areas of differential equations, with emphasis on PDEs, and integral equations, nonlinear analysis, applied functional analysis, theoretical numerical analysis and approximation theory. Areas of application, for instance, include the use of homogenization theory for electromagnetic phenomena, acoustic vibrations and other problems with multiple space and time scales, inverse problems for medical imaging and geophysics, variational methods for moving boundary problems, convex analysis for theoretical mechanics and analytical methods for spatial bio-mathematical models.