A note on energy and cross-helicity conservation in the ideal magnetohydrodynamic equations

被引：0
|
作者：
Ye, Yulin [1 ]
Li, Zilai [2 ]
机构：
[1] Henan Univ, Sch Math & Stat, Kaifeng, Peoples R China
[2] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo, Henan, Peoples R China
来源：
MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2024年 / 47卷 / 16期
基金：
中国国家自然科学基金;
关键词：
cross-helicity conservation; energy conservation; incompressible ideal flows; WEAK SOLUTIONS; EULER; CONJECTURE; REGULARITY;
D O I：
10.1002/mma.10184
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we are concerned with the conservation of total energy and cross-helicity for the weak solutions in the ideal magnetohydrodynamic (MHD) equations. In the spirit of recent works of Berselli (J. Differ. Equ. 368 (2023), 350-375.) and Berselli-Georgiadis (NoDEA Nonlinear Differ. Equ. Appl. 31 (2024), 33), by establishing a new generalized Constantin-E-Titi type commutator estimate to allow us to make full use of the total energy, we extend the previous classical results to a wider range of exponents. These results indicate the role of the time integrability, spatial integrability, and differential regularity of the velocity (magnetic field) in the conserved quantities of weak solutions in the ideal MHD equations.
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页码：12871 / 12882
页数：12
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