A blowup criterion for viscous, compressible, and heat-conductive magnetohydrodynamic flows

作者：Du, Lili; Wang, Yongfu^*

来源：Journal of Mathematical Physics, 2015, 56(9): 091503.

DOI：10.1063/1.4928869

• NAVIER-STOKES EQUATIONS
• GLOBAL WELL-POSEDNESS
• UP CRITERION
• CLASSICAL-SOLUTIONS
• LARGE OSCILLATIONS
• WEAK SOLUTIONS
• REGULARITY
• EXISTENCE
• BREAKDOWN
• EVOLUTION

In this paper, we proved a blowup criterion for the two-dimensional (2D) viscous, compressible, and heat-conducting magnetohydrodynamic (MHD) flows for Cauchy problem, which depends only on the divergence of the velocity vector field, as well as for the case of bounded domain with Dirichlet boundary conditions. This result indicates that the nature of the blowup for compressible models of viscous media in 2D space is similar to the barotropic compressible Navier-Stokes equations and does not depend on further sophistication of the MHD model. More precisely, taking into account the magnetic effects and heat conductivity does not introduce any new features in the blowup mechanism of full MHD flows, especially, which is independent of the temperature and the magnetic field. The results also imply the global regularity of the strong solution to compressible MHD flows, provided that velocity divergence remains bounded.

• 出版日期2015-9
• 单位四川大学