Abstract
In this paper, we study the three-dimensional(3D) compressible magnetohydrodynamic equations. Firstly, we obtain a blow-up criterion for the local strong solutions in terms of the gradient of the velocity, which is similar to the Beal-Kato-Majda criterion(see [1]) for the ideal incompressible flow. Secondly, we extend the well-known Serrin's blow-up criterion for the 3D incompressible Navier-Stokes equations to the 3D compressible magnetohydrodynamic equations. In addition, initial vacuum is allowed in our cases.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
