# American Institute of Mathematical Sciences

January  2016, 15(1): 161-183. doi: 10.3934/cpaa.2016.15.161

## Serrin-type blowup criterion for full compressible Navier-Stokes-Maxwell system with vacuum

 1 School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China, China

Received  August 2015 Revised  September 2015 Published  December 2015

In this paper, we establish a Serrin-type blowup criterion for the Cauchy problem of the three dimensional compressible Navier-Stokes-Maxwell system, which states a classical solution exists globally, provided that the velocity satisfies Serrin's condition and that the $L_t^\infty L_x^\infty$ of density $\rho$ and the $L^2_tL_x^2$ of $\nabla^2 E$ are bounded. In particular, this criterion is analogous to the well-known Serrin's blowup criterion for the three-dimensional compressible Navier-Stokes equations. Moreover, it is independent of the temperature and magnetic field. It should be noted that it is the first result about the possibility of global existence of classical solution for the full Navier-Stokes-Maxwell system.
Citation: Xiaofeng Hou, Limei Zhu. Serrin-type blowup criterion for full compressible Navier-Stokes-Maxwell system with vacuum. Communications on Pure & Applied Analysis, 2016, 15 (1) : 161-183. doi: 10.3934/cpaa.2016.15.161
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