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May  2012, 11(3): 959-971. doi: 10.3934/cpaa.2012.11.959

Large time behavior for the full compressible magnetohydrodynamic flows

Geonho Lee 1, , Sangdong Kim 1, and  Young-Sam Kwon 2,

1. 

Department of Mathematics, Kyungpook National University, Daegu, 702-701, South Korea, South Korea
2. 

Department of Mathematics Dong-A University, Busan 604-714, South Korea

Received  July 2010 Revised  November 2011 Published  December 2011

In this paper we consider the magnetohydrodynamic flows giving rise to a variety of mathematical problems in many areas. We here study the issue of asymptotic analysis of the full magnetohydrodynamics flows and the main idea is based on Feireisl et al [6], [8], [9] for the Navier-Stokes-Fourier systems.
Keywords: compressible viscous fluid., compressible magnetohydrodynamic flows, Large time behavior.
Mathematics Subject Classification: Primary: 35L15; Secondary: 35L5.
Citation: Geonho Lee, Sangdong Kim, Young-Sam Kwon. Large time behavior for the full compressible magnetohydrodynamic flows. Communications on Pure and Applied Analysis, 2012, 11 (3) : 959-971. doi: 10.3934/cpaa.2012.11.959
References:
[1]

E. Becker, "Gasdynamik," Teubner-Verlag, Stuttgart, 1966.

[2]

J. Březina, On Uniqueness of the static state fpr a general compressible fluid, Nonlinear Anal., 64 (2006), 188-195.

[3]

R. Coifman and Y. Meyer, On commutators of singular integrals and bilinear singular integrals, Trans. Amer. Math. Soc., 212 (1975), 315-331.

[4]

B. Ducomet and E. Feireisl, The Equations of magnetohydrodynamics: on the interaction between matter and radiation in the evolution of gaseous stars, Commun. Math. Phys., 266 (2006), 595-629.

[5]

E. Feireisl, Stability of flows of real monoatomic gases, Commun. Partial Differential Equations, 31 (2006), 325-348.

[6]

E. Feireisl and A. Novotný, Large time behaviour of flows of compressible, viscous, heat conducting fluids, Math. Meth. Appl. Sci., 29 (2006), 1237-1260.

[7]

E. Feireisl, A. Novotný and H. Petzeltová, On the existence of globally defined weak solutions to the Navier-Stokes equations of compressible isentropic fluids, J. Math. Fluid Dynamics, 3 (2001), 358-392.

[8]

E. Feireisl and H. Petzeltová, Large-time behaviour of solutions to the Navier-Stokes equations of compressible flow, Arch. Rational Mech. Anal., 150 (1999), 77-96.

[9]

E. Feireisl and H. Petzeltová, On the Long-time behaviour od solutions to the Navier-Stokes-Fourier system with a time-dependent driving force, J. Dynam. Differential Equations, 19 (2007), 685-707.

[10]

E. Feireisl, H. Petzeltová and K. Trivisa, Multicomponent reactive flows: Global-in-time existence for large data, Comm. Pure Appl. Anal., 7 (2008), 1017-1047.

[11]

X. Hu and D. Wang, Global existence and large-time behavior of solutions to the three-dimensional equations of compressible magnetohydrodynamic flows, Arch. Rational Mech. Anal., 197 (2010), 203-238.

[12]

R. Klein, N. Botta, T. Schneider, C. D. Munz, S. Roller, A. Meister, L. Hoffmann and T. Sonar, Asymptotic adaptive methods for multi-scale problems in fluid mechanics, J. Engrg. Math., 39 (2001), 261-343.

[13]

Y.-S. Kwon and K. Trivisa, Stability and large time behavior for multicomponent reactive flows, Nonlinearity, 22 (2009), 2443-2471.

[14]

L. Poul, Existence of weak solutions to the Navier-Stokes-Fourier system on Lipschitz domains, Discr. Cont. Dyn. Syst., 2006. Dynamical Systems and Differential Equations. Proceedings of the 6th AIMS International Conference, suppl., 834-843.

show all references

References:
[1]

E. Becker, "Gasdynamik," Teubner-Verlag, Stuttgart, 1966.

[2]

J. Březina, On Uniqueness of the static state fpr a general compressible fluid, Nonlinear Anal., 64 (2006), 188-195.

[3]

R. Coifman and Y. Meyer, On commutators of singular integrals and bilinear singular integrals, Trans. Amer. Math. Soc., 212 (1975), 315-331.

[4]

B. Ducomet and E. Feireisl, The Equations of magnetohydrodynamics: on the interaction between matter and radiation in the evolution of gaseous stars, Commun. Math. Phys., 266 (2006), 595-629.

[5]

E. Feireisl, Stability of flows of real monoatomic gases, Commun. Partial Differential Equations, 31 (2006), 325-348.

[6]

E. Feireisl and A. Novotný, Large time behaviour of flows of compressible, viscous, heat conducting fluids, Math. Meth. Appl. Sci., 29 (2006), 1237-1260.

[7]

E. Feireisl, A. Novotný and H. Petzeltová, On the existence of globally defined weak solutions to the Navier-Stokes equations of compressible isentropic fluids, J. Math. Fluid Dynamics, 3 (2001), 358-392.

[8]

E. Feireisl and H. Petzeltová, Large-time behaviour of solutions to the Navier-Stokes equations of compressible flow, Arch. Rational Mech. Anal., 150 (1999), 77-96.

[9]

E. Feireisl and H. Petzeltová, On the Long-time behaviour od solutions to the Navier-Stokes-Fourier system with a time-dependent driving force, J. Dynam. Differential Equations, 19 (2007), 685-707.

[10]

E. Feireisl, H. Petzeltová and K. Trivisa, Multicomponent reactive flows: Global-in-time existence for large data, Comm. Pure Appl. Anal., 7 (2008), 1017-1047.

[11]

X. Hu and D. Wang, Global existence and large-time behavior of solutions to the three-dimensional equations of compressible magnetohydrodynamic flows, Arch. Rational Mech. Anal., 197 (2010), 203-238.

[12]

R. Klein, N. Botta, T. Schneider, C. D. Munz, S. Roller, A. Meister, L. Hoffmann and T. Sonar, Asymptotic adaptive methods for multi-scale problems in fluid mechanics, J. Engrg. Math., 39 (2001), 261-343.

[13]

Y.-S. Kwon and K. Trivisa, Stability and large time behavior for multicomponent reactive flows, Nonlinearity, 22 (2009), 2443-2471.

[14]

L. Poul, Existence of weak solutions to the Navier-Stokes-Fourier system on Lipschitz domains, Discr. Cont. Dyn. Syst., 2006. Dynamical Systems and Differential Equations. Proceedings of the 6th AIMS International Conference, suppl., 834-843.

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