Local existence for the non-resistive magnetohydrodynamic system with fractional dissipation in the Lp framework

被引：0
|
作者：
Qiu, Hua [1 ]
Yao, Zheng-an [2 ]
机构：
[1] South China Agr Univ, Dept Math, Guangzhou 510642, Peoples R China
[2] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Peoples R China
来源：
PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2022年 / 3卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Magnetohydrodynamic system; Weak solution; Uniqueness; Besov spaces; GLOBAL SMALL SOLUTIONS; MIXED PARTIAL DISSIPATION; 2D MHD EQUATIONS; WELL-POSEDNESS; WEAK SOLUTIONS; CLASSICAL-SOLUTIONS; REGULARITY; UNIQUENESS; CRITERION;
D O I：
10.1007/s42985-022-00211-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the Cauchy problem of the d-dimensional magnetohydrodynamic (MHD) system with the fractional dissipation (-Delta)(alpha)u and without the magnetic diffusion. We obtain the local existence and uniqueness of the solution to the non-resistive MHD system in the L-P framework under two cases: alpha >= 1 and alpha < 1. Our result improves considerably the recent results in Chemin et al. (Adv Math 286:1-31, 2016), Jiu et al. (Commun Math Sci 18:987-1022, 2020), Li et al. (Adv Math 317:786-798, 2017), and Wan (Nonlinear Anal Real World Appl 30:32-40, 2016), which can be regarded as a generalization of these works.
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页数：38
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