Energy conservation for the weak solutions to the 3D compressible magnetohydrodynamic equations of viscous non-resistive fluids in a bounded domain

作者：Wang, Xiong; Liu, Sili^*

来源：NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2021, 62: 103359.

DOI：10.1016/j.nonrwa.2021.103359

• Compressible MHD equations
• Viscous non-resistive fluids
• Bounded domain
• Weak solutions
• Energy conservation

In this paper, inspired by the work of Chen-Liang-Wang-Xu (Chen et al., 2020) on compressible Navier-Stokes equations, we obtain the energy conservation for weak solutions of the compressible non-resistive magnetohydrodynamic flows in a bounded domain Omega subset of R-3. To ensure the energy conservation, we need the same regularity conditions of density and velocity as in Chen et al. (2020), moreover, H is an element of L-t(4) L-x(4) and del H is an element of L-t(p1) L-x(q1), where p1 = 3p/3p-4 , q1 = 4q/3q-4. Under these conditions, p1 is an element of (4/3, 2], q1 is an element of (4/3, 12/7] when p >= 4 and q >= 6.