1. A note on energy and cross‐helicity conservation in the ideal magnetohydrodynamic equations.
- Author
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Ye, Yulin and Li, Zilai
- Subjects
- *
ENERGY conservation , *INCOMPRESSIBLE flow , *CONSERVED quantity , *ENERGY consumption , *MAGNETIC fields - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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