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

Xiaofeng  Hou; Limei  Zhu

doi:10.3934/cpaa.2016.15.161

Article Contents

2016, Volume 15, Issue 1: 161-183. Doi: 10.3934/cpaa.2016.15.161

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

Xiaofeng Hou^1, and
Limei Zhu^1,

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

Received: July 31, 2015

Revised: August 31, 2015

Published: December 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 76X05, 76N10, 35L65.

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