• Previous Article
    A new blowup criterion for strong solutions to a viscous liquid-gas two-phase flow model with vacuum in three dimensions
  • KRM Home
  • This Issue
  • Next Article
    Separated characteristics and global solvability for the one and one-half dimensional Vlasov Maxwell system
2016, 9(3): 443-453. doi: 10.3934/krm.2016002

Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations in a bounded domain

1. 

Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037

2. 

Department of Mathematics, Nanjing University, Nanjing 210093

3. 

Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan

Received  April 2015 Revised  October 2015 Published  May 2016

In this paper we establish the uniform estimates of strong solutions with respect to the Mach number and the dielectric constant to the full compressible Navier-Stokes-Maxwell system in a bounded domain. Based on these uniform estimates, we obtain the convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations for well-prepared data.
Citation: Jishan Fan, Fucai Li, Gen Nakamura. Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations in a bounded domain. Kinetic & Related Models, 2016, 9 (3) : 443-453. doi: 10.3934/krm.2016002
References:
[1]

T. Alazard, Low Mach number limit of the full Navier-Stokes equations,, Arch. Ration. Mech. Anal., 180 (2006), 1. doi: 10.1007/s00205-005-0393-2.

[2]

J. Bourguignon and H. Brezis, Remarks on the Euler equation,, J. Funct. Anal., 15 (1974), 341. doi: 10.1016/0022-1236(74)90027-5.

[3]

W. Cui, Y. Ou and D. Ren, Incompressible limit of full compressible magnetohydrodynamic equations with well-prepared data in 3-D bounded domains,, J. Math. Anal. Appl., 427 (2015), 263. doi: 10.1016/j.jmaa.2015.02.049.

[4]

C. Dou, S. Jiang and Y. Ou, Low Mach number limit of full Navier-Stokes equations in a 3D bounded domain,, J. Differential Equations, 258 (2015), 379. doi: 10.1016/j.jde.2014.09.017.

[5]

J. Fan, F. Li and G. Nakamura, Uniform well-posedness and singular limits of the isentropic Navier-Stokes-Maxwell system in a bounded domain,, Z. Angew. Math. Phys., 66 (2015), 1581. doi: 10.1007/s00033-014-0484-8.

[6]

I. Imai, General principles of magneto-fluid dynamics,, in Magneto-Fluid Dynamics, (1962), 1.

[7]

S. Jiang and F. Li, Convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations,, Asymptot. Anal., 95 (2015), 161. doi: 10.3233/ASY-151321.

[8]

S. Jiang and F. Li, Zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system,, Sci. China Math., 58 (2015), 61. doi: 10.1007/s11425-014-4923-y.

[9]

S. Kawashima and Y. Shizuta, Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid,, Tsukuba J. Math., 10 (1986), 131.

[10]

S. Kawashima and Y. Shizuta, Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid II,, Proc. Japan Acad., 62 (1986), 181. doi: 10.3792/pjaa.62.181.

[11]

F. Li and Y. Mu, Low Mach number limit of the full compressible Navier-Stokes-Maxwell system,, J. Math. Anal. Appl., 412 (2014), 334. doi: 10.1016/j.jmaa.2013.10.064.

[12]

G. Metivier and S. Schochet, The incompressible limit of the non-isentropic Euler equations,, Arch. Ration. Mech. Anal., 158 (2001), 61. doi: 10.1007/PL00004241.

[13]

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. doi: 10.1002/cpa.20187.

[14]

W. M. Zajaczkowski, On nonstationary motion of a compressible barotropic viscous fluid with boundary slip condition,, J. Appl. Anal., 4 (1998), 167. doi: 10.1515/JAA.1998.167.

show all references

References:
[1]

T. Alazard, Low Mach number limit of the full Navier-Stokes equations,, Arch. Ration. Mech. Anal., 180 (2006), 1. doi: 10.1007/s00205-005-0393-2.

[2]

J. Bourguignon and H. Brezis, Remarks on the Euler equation,, J. Funct. Anal., 15 (1974), 341. doi: 10.1016/0022-1236(74)90027-5.

[3]

W. Cui, Y. Ou and D. Ren, Incompressible limit of full compressible magnetohydrodynamic equations with well-prepared data in 3-D bounded domains,, J. Math. Anal. Appl., 427 (2015), 263. doi: 10.1016/j.jmaa.2015.02.049.

[4]

C. Dou, S. Jiang and Y. Ou, Low Mach number limit of full Navier-Stokes equations in a 3D bounded domain,, J. Differential Equations, 258 (2015), 379. doi: 10.1016/j.jde.2014.09.017.

[5]

J. Fan, F. Li and G. Nakamura, Uniform well-posedness and singular limits of the isentropic Navier-Stokes-Maxwell system in a bounded domain,, Z. Angew. Math. Phys., 66 (2015), 1581. doi: 10.1007/s00033-014-0484-8.

[6]

I. Imai, General principles of magneto-fluid dynamics,, in Magneto-Fluid Dynamics, (1962), 1.

[7]

S. Jiang and F. Li, Convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations,, Asymptot. Anal., 95 (2015), 161. doi: 10.3233/ASY-151321.

[8]

S. Jiang and F. Li, Zero dielectric constant limit to the non-isentropic compressible Euler-Maxwell system,, Sci. China Math., 58 (2015), 61. doi: 10.1007/s11425-014-4923-y.

[9]

S. Kawashima and Y. Shizuta, Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid,, Tsukuba J. Math., 10 (1986), 131.

[10]

S. Kawashima and Y. Shizuta, Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid II,, Proc. Japan Acad., 62 (1986), 181. doi: 10.3792/pjaa.62.181.

[11]

F. Li and Y. Mu, Low Mach number limit of the full compressible Navier-Stokes-Maxwell system,, J. Math. Anal. Appl., 412 (2014), 334. doi: 10.1016/j.jmaa.2013.10.064.

[12]

G. Metivier and S. Schochet, The incompressible limit of the non-isentropic Euler equations,, Arch. Ration. Mech. Anal., 158 (2001), 61. doi: 10.1007/PL00004241.

[13]

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. doi: 10.1002/cpa.20187.

[14]

W. M. Zajaczkowski, On nonstationary motion of a compressible barotropic viscous fluid with boundary slip condition,, J. Appl. Anal., 4 (1998), 167. doi: 10.1515/JAA.1998.167.

[1]

Jishan Fan, Fucai Li, Gen Nakamura. Global existence and low Mach number limit to the 3D compressible magnetohydrodynamic equations in a bounded domain. Conference Publications, 2015, 2015 (special) : 387-394. doi: 10.3934/proc.2015.0387

[2]

Fucai Li, Yanmin Mu. Low Mach number limit for the compressible magnetohydrodynamic equations in a periodic domain. Discrete & Continuous Dynamical Systems - A, 2018, 38 (4) : 1669-1705. doi: 10.3934/dcds.2018069

[3]

Jishan Fan, Fucai Li, Gen Nakamura. Low Mach number limit of the full compressible Hall-MHD system. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1731-1740. doi: 10.3934/cpaa.2017084

[4]

Jingrui Su. Global existence and low Mach number limit to a 3D compressible micropolar fluids model in a bounded domain. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 3423-3434. doi: 10.3934/dcds.2017145

[5]

Weike Wang, Xin Xu. Large time behavior of solution for the full compressible navier-stokes-maxwell system. Communications on Pure & Applied Analysis, 2015, 14 (6) : 2283-2313. doi: 10.3934/cpaa.2015.14.2283

[6]

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

[7]

Jishan Fan, Yueling Jia. Local well-posedness of the full compressible Navier-Stokes-Maxwell system with vacuum. Kinetic & Related Models, 2018, 11 (1) : 97-106. doi: 10.3934/krm.2018005

[8]

Fucai Li, Yanmin Mu, Dehua Wang. Local well-posedness and low Mach number limit of the compressible magnetohydrodynamic equations in critical spaces. Kinetic & Related Models, 2017, 10 (3) : 741-784. doi: 10.3934/krm.2017030

[9]

Guangrong Wu, Ping Zhang. The zero diffusion limit of 2-D Navier-Stokes equations with $L^1$ initial vorticity. Discrete & Continuous Dynamical Systems - A, 1999, 5 (3) : 631-638. doi: 10.3934/dcds.1999.5.631

[10]

Jishan Fan, Fucai Li, Gen Nakamura. A regularity criterion for the 3D full compressible magnetohydrodynamic equations with zero heat conductivity. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1757-1766. doi: 10.3934/dcdsb.2018079

[11]

Jianwei Yang, Ruxu Lian, Shu Wang. Incompressible type euler as scaling limit of compressible Euler-Maxwell equations. Communications on Pure & Applied Analysis, 2013, 12 (1) : 503-518. doi: 10.3934/cpaa.2013.12.503

[12]

Zhong Tan, Leilei Tong. Asymptotic behavior of the compressible non-isentropic Navier-Stokes-Maxwell system in $\mathbb{R}^3$. Kinetic & Related Models, 2018, 11 (1) : 191-213. doi: 10.3934/krm.2018010

[13]

Thomas Alazard. A minicourse on the low Mach number limit. Discrete & Continuous Dynamical Systems - S, 2008, 1 (3) : 365-404. doi: 10.3934/dcdss.2008.1.365

[14]

Donatella Donatelli, Bernard Ducomet, Šárka Nečasová. Low Mach number limit for a model of accretion disk. Discrete & Continuous Dynamical Systems - A, 2018, 38 (7) : 3239-3268. doi: 10.3934/dcds.2018141

[15]

Linjie Xiong. Incompressible Limit of isentropic Navier-Stokes equations with Navier-slip boundary. Kinetic & Related Models, 2018, 11 (3) : 469-490. doi: 10.3934/krm.2018021

[16]

Matthew Paddick. The strong inviscid limit of the isentropic compressible Navier-Stokes equations with Navier boundary conditions. Discrete & Continuous Dynamical Systems - A, 2016, 36 (5) : 2673-2709. doi: 10.3934/dcds.2016.36.2673

[17]

Jiang Xu, Ting Zhang. Zero-electron-mass limit of Euler-Poisson equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (10) : 4743-4768. doi: 10.3934/dcds.2013.33.4743

[18]

Gaocheng Yue, Chengkui Zhong. On the global well-posedness to the 3-D Navier-Stokes-Maxwell system. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5817-5835. doi: 10.3934/dcds.2016056

[19]

Li Fang, Zhenhua Guo. Zero dissipation limit to rarefaction wave with vacuum for a one-dimensional compressible non-Newtonian fluid. Communications on Pure & Applied Analysis, 2017, 16 (1) : 209-242. doi: 10.3934/cpaa.2017010

[20]

Yanmin Mu. Convergence of the compressible isentropic magnetohydrodynamic equations to the incompressible magnetohydrodynamic equations in critical spaces. Kinetic & Related Models, 2014, 7 (4) : 739-753. doi: 10.3934/krm.2014.7.739

2016 Impact Factor: 1.261

Metrics

  • PDF downloads (2)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]