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Incompressible limit for the full magnetohydrodynamics flows under Strong Stratification on unbounded domains
1. | Department of Applied Mathematics, Changwon National University, Changwon 641-773, South Korea |
2. | Department of Mathematics Dong-A University, Busan 604-714 |
References:
[1] | |
[2] |
B. Ducomet and E. Feireisl, The equations of magnetohydrodynamics: on the interaction between matter and radiation in the evolution of gaseous stars, Comm. Math. Phys., 266 (2006), 595-625.
doi: 10.1007/s00220-006-0052-y. |
[3] |
S. Eliezer, A. Ghatak and H. Hora, "An Introduction to Equations of States, Theory and Applications," Cambridge University Press, Cambridge, 1986. |
[4] |
E. Feireisl, Incompressible limits and propagation of acoustic waves in large domains with boundaries, Comm. Math. Phys., 294 (2010), 73-95.
doi: 10.1007/s00220-009-0954-6. |
[5] |
E. Feireisl, Stability of flows of real monoatomic gases, Commun. Partial Differential Equations, 31 (2006), 325-348.
doi: 10.1080/03605300500358186. |
[6] |
E. Feireisl and A. Novotný, The low Mach number limit for the full Navier-Stokes-Fourier system, Arch. Ration. Mech. Ana., 186 (2007), 77-107.
doi: 10.1007/s00205-007-0066-4. |
[7] |
E. Feireisl and A. Novotný, "Singular Limit in the Thermodynamics of Viscous Fluids," Advanceds in Mathematical Fluid Mechanics, 2009.
doi: 10.1007/978-3-7643-8843-0. |
[8] |
E. Feireisl, A. Novotný} and H. Petzeltová, Low Mach number limt for the Navier-Stokes system on unbounded domains under strong stratification, Comm. P.D.E., 35 (2010), 68-88.
doi: 10.1080/03605300903279377. |
[9] |
X. Hu and D. Wang, Global solutions to the three-dimensional full compressible magnetohydrodynamic flows, Comm. Math. Phys., 283 (2008), 255-284.
doi: 10.1007/s00220-008-0497-2. |
[10] |
S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Comm. Pure Appl. Math., 34 (1981), 481-524.
doi: 10.1002/cpa.3160340405. |
[11] |
Y.-S. Kwon and K. Trivisa, On the incompressible limits for the full magnetohydrodynamics flows, J. Differential Equations., 251 (2011), 1990-2023.
doi: 10.1016/j.jde.2011.04.016. |
[12] |
Peter Kukucka, Singular Limits of the Equations of Magnetohydrodynamics, J. Math. Fluid Mech., 13 (2011), 173-189.
doi: 10.1007/s00021-009-0007-0. |
[13] |
G. Lee, P. Kim and Y.-S. Kwon, Incompressible limit for the full magnetohydrodynamics flows under strong stratification, J. Math. Anal. Appl., 387 (2012), 221-240.
doi: 10.1016/j.jmaa.2011.08.070. |
[14] |
P.-L. Lions and N. Masmoudi, Incompressible limit for a viscous compressible fluid, J. Math. Pures Appl., 77 (1998), 585-627.
doi: 10.1016/S0021-7824(98)80139-6. |
[15] |
A. Novotný, M. Ruzicka and G. Thater, Rigorous derivation of the anelastic approximation to the Oberbeck-Boussinesq equations, Asymptot. Anal., 75 (2011), 93-123. |
[16] |
A. Novotný, M. Ruzicka and G. Thater, Singular limit of the equations of magnetohydrodynamics in the presence of strong stratification, Math. Models Methods Appl. Sci., 21 (2011), 115-147.
doi: 10.1142/S0218202511005003. |
[17] |
M. Reed and B. Simon, "Methods of Modern Mathematical Physics.IV. Analysis of Operator," New York: Academy Press [Harcourt Brace Jovanovich Publishers], 1978. |
show all references
References:
[1] | |
[2] |
B. Ducomet and E. Feireisl, The equations of magnetohydrodynamics: on the interaction between matter and radiation in the evolution of gaseous stars, Comm. Math. Phys., 266 (2006), 595-625.
doi: 10.1007/s00220-006-0052-y. |
[3] |
S. Eliezer, A. Ghatak and H. Hora, "An Introduction to Equations of States, Theory and Applications," Cambridge University Press, Cambridge, 1986. |
[4] |
E. Feireisl, Incompressible limits and propagation of acoustic waves in large domains with boundaries, Comm. Math. Phys., 294 (2010), 73-95.
doi: 10.1007/s00220-009-0954-6. |
[5] |
E. Feireisl, Stability of flows of real monoatomic gases, Commun. Partial Differential Equations, 31 (2006), 325-348.
doi: 10.1080/03605300500358186. |
[6] |
E. Feireisl and A. Novotný, The low Mach number limit for the full Navier-Stokes-Fourier system, Arch. Ration. Mech. Ana., 186 (2007), 77-107.
doi: 10.1007/s00205-007-0066-4. |
[7] |
E. Feireisl and A. Novotný, "Singular Limit in the Thermodynamics of Viscous Fluids," Advanceds in Mathematical Fluid Mechanics, 2009.
doi: 10.1007/978-3-7643-8843-0. |
[8] |
E. Feireisl, A. Novotný} and H. Petzeltová, Low Mach number limt for the Navier-Stokes system on unbounded domains under strong stratification, Comm. P.D.E., 35 (2010), 68-88.
doi: 10.1080/03605300903279377. |
[9] |
X. Hu and D. Wang, Global solutions to the three-dimensional full compressible magnetohydrodynamic flows, Comm. Math. Phys., 283 (2008), 255-284.
doi: 10.1007/s00220-008-0497-2. |
[10] |
S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Comm. Pure Appl. Math., 34 (1981), 481-524.
doi: 10.1002/cpa.3160340405. |
[11] |
Y.-S. Kwon and K. Trivisa, On the incompressible limits for the full magnetohydrodynamics flows, J. Differential Equations., 251 (2011), 1990-2023.
doi: 10.1016/j.jde.2011.04.016. |
[12] |
Peter Kukucka, Singular Limits of the Equations of Magnetohydrodynamics, J. Math. Fluid Mech., 13 (2011), 173-189.
doi: 10.1007/s00021-009-0007-0. |
[13] |
G. Lee, P. Kim and Y.-S. Kwon, Incompressible limit for the full magnetohydrodynamics flows under strong stratification, J. Math. Anal. Appl., 387 (2012), 221-240.
doi: 10.1016/j.jmaa.2011.08.070. |
[14] |
P.-L. Lions and N. Masmoudi, Incompressible limit for a viscous compressible fluid, J. Math. Pures Appl., 77 (1998), 585-627.
doi: 10.1016/S0021-7824(98)80139-6. |
[15] |
A. Novotný, M. Ruzicka and G. Thater, Rigorous derivation of the anelastic approximation to the Oberbeck-Boussinesq equations, Asymptot. Anal., 75 (2011), 93-123. |
[16] |
A. Novotný, M. Ruzicka and G. Thater, Singular limit of the equations of magnetohydrodynamics in the presence of strong stratification, Math. Models Methods Appl. Sci., 21 (2011), 115-147.
doi: 10.1142/S0218202511005003. |
[17] |
M. Reed and B. Simon, "Methods of Modern Mathematical Physics.IV. Analysis of Operator," New York: Academy Press [Harcourt Brace Jovanovich Publishers], 1978. |
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