Energy conservation for the weak solutions to the ideal inhomogeneous magnetohydrodynamic equations in a bounded domain. (February 2022)

• Record Type: Journal Article
• Authors: Zhang, Zhipeng
• Is Part Of: Nonlinear analysis. Volume 63(2022)
• Publication Date: 2022-02
• Subjects: Ideal inhomogeneous magnetohydrodynamic equations -- Weak solution -- Energy conservation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103397
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we prove the energy conservation for the weak solutions of the three-dimensional ideal inhomogeneous magnetohydrodynamic (MHD) equations in a bounded domain. Two types of sufficient conditions on the regularity of the weak solutions are provided to ensure the energy conservation. Due to the presence of the boundary, we need to impose the boundedness in L p and the continuity in L p p − 2 for the velocity and magnetic fields near the boundary.