Energy conservation for weak solutions to two-phase magnetohydrodynamic flows

Abstract

In this paper, we consider the energy conservation of weak solutions to the two-phase magnetohydrodynamic flows in a bounded domain. We establish the Shinbrot-type regularity condition to ensure the energy conservation for a weak solution, which extends/improves previous various energy conservation works on Navier-Stokes-Cahn-Hilliard equations and MHD equations.

Keywords:

• Energy conservation
• weak solutions
• two-phase magnetohydrodynamic flows
• bounded domain

2020 Mathematics Subject Classifications:

• 76W05
• 76B03
• 35Q35

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Additional information

Funding

F. Wu was supported by the Jiangxi Provincial Natural Science Foundation [grant number 20224BAB211003], the Science and Technology Project of Jiangxi Provincial Department of Education [grant number GJJ2201524] and the doctoral research start-up project of Nanchang Institute of Technology [grant number 2022kyqd044].