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A new blowup criterion for strong solutions to a viscous liquid-gas two-phase flow model with vacuum in three dimensions
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 |
References:
[1] |
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. |
[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. |
[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), 263-288.
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), 379-398.
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), 1581-1593.
doi: 10.1007/s00033-014-0484-8. |
[6] |
I. Imai, General principles of magneto-fluid dynamics, in Magneto-Fluid Dynamics, Suppl. Prog. Theor. Phys. No.24 (ed. H. Yukawa), RIFP Kyoto Univ., (1962), Chap. I, 1-34. |
[7] |
S. Jiang and F. Li, Convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations, Asymptot. Anal., 95 (2015), 161-185.
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), 61-76.
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), 131-149. |
[10] |
S. Kawashima and Y. Shizuta, Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid II, Proc. Japan Acad., Ser. A, 62 (1986), 181-184.
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), 334-344.
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), 61-90.
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), 1027-1055.
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), 167-204.
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), 1-73.
doi: 10.1007/s00205-005-0393-2. |
[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. |
[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), 263-288.
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), 379-398.
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), 1581-1593.
doi: 10.1007/s00033-014-0484-8. |
[6] |
I. Imai, General principles of magneto-fluid dynamics, in Magneto-Fluid Dynamics, Suppl. Prog. Theor. Phys. No.24 (ed. H. Yukawa), RIFP Kyoto Univ., (1962), Chap. I, 1-34. |
[7] |
S. Jiang and F. Li, Convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations, Asymptot. Anal., 95 (2015), 161-185.
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), 61-76.
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), 131-149. |
[10] |
S. Kawashima and Y. Shizuta, Magnetohydrodynamic approximation of the complete equations for an electromagnetic fluid II, Proc. Japan Acad., Ser. A, 62 (1986), 181-184.
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), 334-344.
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), 61-90.
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), 1027-1055.
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), 167-204.
doi: 10.1515/JAA.1998.167. |
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