Local well-posedness of the full compressible Navier-Stokes-Maxwell system with vacuum

Jishan Fan; Yueling Jia

doi:10.3934/krm.2018005

Article Contents

2018, Volume 11, Issue 2: 1-10. Doi: 10.3934/krm.2018005

This issue Previous Article Dynamical pressure in a polyatomic gas: Interplay between kinetic theory and extended thermodynamics Next Article Non-contraction of intermediate admissible discontinuities for 3-D planar isentropic magnetohydrodynamics

Local well-posedness of the full compressible Navier-Stokes-Maxwell system with vacuum

Jishan Fan^1, and
Yueling Jia^2, ,

1.
Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China
2.
Institute of Applied Physics and Computational Mathematics, FengHao East Road, Haidian District, Beijing 100094, China

* Corresponding author: Yueling Jia
* Corresponding author: Yueling Jia

Received: December 2016

Revised: March 2017

Published: April 2018

This work is supported by NSFC grant No.11171154, 11271051

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Abstract

In this paper, we prove the local well-posedness of strong solutions for a compressible Navier-Stokes-Maxwell system, provided the initial data satisfy a natural compatibility condition. We do not assume the positivity of initial density, it may vanish in an open subset (vacuum) of Ω.

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Mathematics Subject Classification: Primary:35Q30, 35Q35, 35B25;Secondary:76W05.

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