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

Large time behavior for the full compressible magnetohydrodynamic flows

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.
Citation: Geonho Lee, Sangdong Kim, Young-Sam Kwon. Large time behavior for the full compressible magnetohydrodynamic flows. Communications on Pure & Applied Analysis, 2012, 11 (3) : 959-971. doi: 10.3934/cpaa.2012.11.959
References:
[1]

E. Becker, "Gasdynamik,", Teubner-Verlag, (1966). Google Scholar

[2]

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

[3]

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

[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. Google Scholar

[5]

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

[6]

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

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[13]

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

[14]

L. Poul, Existence of weak solutions to the Navier-Stokes-Fourier system on Lipschitz domains,, Discr. Cont. Dyn. Syst., (2006), 834. Google Scholar

show all references

References:
[1]

E. Becker, "Gasdynamik,", Teubner-Verlag, (1966). Google Scholar

[2]

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

[3]

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

[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. Google Scholar

[5]

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

[6]

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

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[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. Google Scholar

[13]

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

[14]

L. Poul, Existence of weak solutions to the Navier-Stokes-Fourier system on Lipschitz domains,, Discr. Cont. Dyn. Syst., (2006), 834. Google Scholar

[1]

Chiu-Ya Lan, Chi-Kun Lin. Asymptotic behavior of the compressible viscous potential fluid: Renormalization group approach. Discrete & Continuous Dynamical Systems - A, 2004, 11 (1) : 161-188. doi: 10.3934/dcds.2004.11.161

[2]

Hong Cai, Zhong Tan. Time periodic solutions to the three--dimensional equations of compressible magnetohydrodynamic flows. Discrete & Continuous Dynamical Systems - A, 2016, 36 (4) : 1847-1868. doi: 10.3934/dcds.2016.36.1847

[3]

Tong Tang, Hongjun Gao. Local strong solutions to the compressible viscous magnetohydrodynamic equations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1617-1633. doi: 10.3934/dcdsb.2016014

[4]

Huicheng Yin, Lin Zhang. The global existence and large time behavior of smooth compressible fluid in an infinitely expanding ball, Ⅱ: 3D Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2018, 38 (3) : 1063-1102. doi: 10.3934/dcds.2018045

[5]

Zhong Tan, Yong Wang, Fanhui Xu. Large-time behavior of the full compressible Euler-Poisson system without the temperature damping. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1583-1601. doi: 10.3934/dcds.2016.36.1583

[6]

Shifeng Geng, Lina Zhang. Large-time behavior of solutions for the system of compressible adiabatic flow through porous media with nonlinear damping. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2211-2228. doi: 10.3934/cpaa.2014.13.2211

[7]

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

[8]

Zhong Tan, Yong Wang, Xu Zhang. Large time behavior of solutions to the non-isentropic compressible Navier-Stokes-Poisson system in $\mathbb{R}^{3}$. Kinetic & Related Models, 2012, 5 (3) : 615-638. doi: 10.3934/krm.2012.5.615

[9]

Zhenhua Guo, Wenchao Dong, Jinjing Liu. Large-time behavior of solution to an inflow problem on the half space for a class of compressible non-Newtonian fluids. Communications on Pure & Applied Analysis, 2019, 18 (4) : 2133-2161. doi: 10.3934/cpaa.2019096

[10]

Cristian A. Coclici, Jörg Heiermann, Gh. Moroşanu, W. L. Wendland. Asymptotic analysis of a two--dimensional coupled problem for compressible viscous flows. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 137-163. doi: 10.3934/dcds.2004.10.137

[11]

Takayuki Kubo, Yoshihiro Shibata, Kohei Soga. On some two phase problem for compressible and compressible viscous fluid flow separated by sharp interface. Discrete & Continuous Dynamical Systems - A, 2016, 36 (7) : 3741-3774. doi: 10.3934/dcds.2016.36.3741

[12]

Eduard Feireisl, Hana Petzeltová. Low Mach number asymptotics for reacting compressible fluid flows. Discrete & Continuous Dynamical Systems - A, 2010, 26 (2) : 455-480. doi: 10.3934/dcds.2010.26.455

[13]

Dongfen Bian, Boling Guo. Global existence and large time behavior of solutions to the electric-magnetohydrodynamic equations. Kinetic & Related Models, 2013, 6 (3) : 481-503. doi: 10.3934/krm.2013.6.481

[14]

Jishan Fan, Shuxiang Huang, Fucai Li. Global strong solutions to the planar compressible magnetohydrodynamic equations with large initial data and vacuum. Kinetic & Related Models, 2017, 10 (4) : 1035-1053. doi: 10.3934/krm.2017041

[15]

Eduard Feireisl, Dalibor Pražák. A stabilizing effect of a high-frequency driving force on the motion of a viscous, compressible, and heat conducting fluid. Discrete & Continuous Dynamical Systems - S, 2009, 2 (1) : 95-111. doi: 10.3934/dcdss.2009.2.95

[16]

Bernard Ducomet, Šárka Nečasová. On the motion of rigid bodies in an incompressible or compressible viscous fluid under the action of gravitational forces. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1193-1213. doi: 10.3934/dcdss.2013.6.1193

[17]

W. Wei, Yin Li, Zheng-An Yao. Decay of the compressible viscoelastic flows. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1603-1624. doi: 10.3934/cpaa.2016004

[18]

Zefu Feng, Changjiang Zhu. Global classical large solution to compressible viscous micropolar and heat-conducting fluids with vacuum. Discrete & Continuous Dynamical Systems - A, 2019, 39 (6) : 3069-3097. doi: 10.3934/dcds.2019127

[19]

Xin Liu. Compressible viscous flows in a symmetric domain with complete slip boundary: The nonlinear stability of uniformly rotating states with small angular velocities. Communications on Pure & Applied Analysis, 2019, 18 (2) : 751-794. doi: 10.3934/cpaa.2019037

[20]

Qing Chen, Zhong Tan. Global existence in critical spaces for the compressible magnetohydrodynamic equations. Kinetic & Related Models, 2012, 5 (4) : 743-767. doi: 10.3934/krm.2012.5.743

2018 Impact Factor: 0.925

Metrics

  • PDF downloads (9)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]