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

Abstract / Introduction Full Text(HTML) Related Papers Cited by

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.

Keywords:

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

Citation:

Full Text(HTML)

Related Papers

Cited by

References

	T. Alazard , Low mach number limit of the full Navier-Stokes equations, Arch. Ration. Mech. Anal., 180 (2006) , 1-73. doi: 10.1007/s00205-005-0393-2.
	J. Bourguignon and H. Brezis , Remarks on the Euler equation, J. Funct. Anal., 15 (1974) , 341-363. doi: 10.1016/0022-1236(74)90027-5.
	Y. Cho and H. Kim , Existence results for viscous polytropic fluid with vacuum, J. Differential Equations, 228 (2006) , 377-411. doi: 10.1016/j.jde.2006.05.001.
	C. Dou , S. Jiang and Y. Ou , Low mach number limit of full Navier-Stokes equations in a 3D bounded domain, J. Diff. Eqs., 258 (2015) , 379-398. doi: 10.1016/j.jde.2014.09.017.
	R. J. Duan , Green's function and large time behavior of the Navier-Stokes-Maxwell system, Anal. Appl., 10 (2012) , 133-197. doi: 10.1142/S0219530512500078.
	J. Fan and W. Yu , Strong solutions to the compressible magnetohydrodynamic equations with vacuum, Nonlinear Analysis-Real World Applications, 10 (2009) , 392-409. doi: 10.1016/j.nonrwa.2007.10.001.
	J. Fan , F. Li and G. Nakamura , Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydarodynamic equations in a bounded domain, Kinet. Relat. Models, 9 (2016) , 443-453. doi: 10.3934/krm.2016002.
	J. Fan , F. Li and G. Nakamura , Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydarodynamic equations in a bounded domain Ⅱ: global existence case, J. Math. Fluid Mech., 9 (2016) , 443-453. doi: 10.3934/krm.2016002.
	Y. H. Feng , S. Wang and X. Li , Asymptotic behavior of global smooth solutions for bipolar compressible Navier-Stokes-Maxwell system from plasmas, Acta Mathematica Scientia, 35 (2015) , 955-969. doi: 10.1016/S0252-9602(15)30030-8.
	G. Y. Hong , X. F. Hou , H. Y. Peng and C. J. Zhu , Global spherically symmetric classical solution to the Navier-Stokes-Maxwell system with large initial data and vacuum, Sci. China Math., 57 (2014) , 2463-2484. doi: 10.1007/s11425-014-4896-x.
	X. Hou and L. Zhu , Serrin-type blowup criterion for full compressible Navier-Stokes-Maxwell system with vacuum, Commun. Pure Appl. Anal., 15 (2016) , 161-183. doi: 10.3934/cpaa.2016.15.161.
	X. F. Hou , L. Yao and C. J. Zhu , Existence and uniqueness of global strong solutions to the Navier-Stokes-Maxwell system with large initial data and vacuum, Scientia Sinica Mathematica, 46 (2016) , 945-966.
	I. Imai, General Principles of Magneto-Fluid Dynamics in "Magneto-Fluid Dynamics, " Suppl. Prog. Theor. Phys. 24(ed. H. Yukawa) Chap. Ⅰ, RIFP Kyoto Univ. , 1962.
	S. Jiang and F. C. Li , Converagese of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations, Asymptotic Analysis, 95 (2015) , 161-185. doi: 10.3233/ASY-151321.
	S. Jiang and F. C. Li , Zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system, Sci. China Math., 58 (2015) , 61-76. doi: 10.1007/s11425-014-4923-y.
	E. Kang and J. Lee, Notes on the global well-posedness for the Maxwell-Navier-Stokes system, Abstract and Applied Analysis 2013 (2013), Art. ID 402793, 6 pp.
	S. Kawashima and Y. Shizuta , Magnetohydrodynamic approximation of the complete equations for an eletromagnetic fluid, Tsukuba J. Math., 10 (1986) , 131-149. doi: 10.21099/tkbjm/1496160397.
	S. Kawashima and Y. Shizuta , Magnetohydrodynamic approximation of the complete equations for an eletromagnetic fluid Ⅱ, Proc. Japan Acad., 62 (1986) , 181-184. doi: 10.3792/pjaa.62.181.
	N. A. Krall and A. W. Trivelpiece, Principles of Plasma Physics San Francisco Press, 1986.
	F. C. Li and Y. Mu , Low mach number limit of the full compressible Navier-Stokes-Maxwell system, J. Math. Anal. Appl., 412 (2014) , 334-344. doi: 10.1016/j.jmaa.2013.10.064.
	E. H. Lieb and M. Loss, Analysis 2$^{nd}$ edition, AMS, 2001.
	P. L. Lions, Mathematical Topics in Fluid Mechanics, vol. 2, Compressible Models Oxford University Press, New York, 1998.
	Q. Q. Liu and Y. F. Su , Large time behavior for the non-isentropic Navier-Stokes-Maxwell system, Mathematical Methods in the Applied Sciences, 40 (2017) , 663-679. doi: 10.1002/mma.3999.
	G. Metivier and S. Schochet , The incompressible limit of the non-isentropic Euler equations, Arch. Ration. Mech. Anal., 158 (2001) , 61-90. doi: 10.1007/PL00004241.
	S. -I. Pai, Magnetogasdynamics and Plasma Dynamics Springer-Verlag, Vienna, 1962.
	W. K. Wang and X. Xu , Large time behavior of solution for the full compressible navier-stokes-maxwell system, Commun. Pure Appl. Anal., 14 (2015) , 2283-2313. doi: 10.3934/cpaa.2015.14.2283.
	Y. Xiao and Z. Xin , On the vanishing viscosity limit for the 3D Navier-Stokes equations with a slip boundary condition, Comm. Pure Appl. Math., 60 (2007) , 1027-1055. doi: 10.1002/cpa.20187.
	W. M. Zajaczkowski , On nonstationary motioni of a compressible barotropic viscous fluid with boundary slip condition, J. Appl. Anal., 4 (1998) , 167-204. doi: 10.1515/JAA.1998.167.