A Beale-Kato-Majda criterion for three dimensional compressible viscous non-isentropic magnetohydrodynamic flows without heat-conductivity

In this paper, we prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth (strong) solutions for the three dimensional (3D) compressible nonisentropic magnetohydrodynamic (MHD) equations with zero heat-conductivity. Therefore, if the maximum norm of the deformation tensor of velocity gradients remains bounded, it is not possible for other kinds of singularities. Our results are same as Beale-Kato-Majda type criterion for compressible viscous barotropic flows (Huang et al., 2011 [17]), and do not depend on further sophistication of the non-isentropic MHD model, it is independent of the pressure and magnetic field. Furthermore, this extends the corresponding Zhong's results (Zhong, 2019 [46]), and removes the viscous coefficients restriction condition 3 mu > lambda and the boundedness of pressure. As a byproduct, the same results also hold for compressible non-isentropic Navier-Stokes equations without heat-conductivity. (C) 2021 Elsevier Inc. All rights reserved.