Global existence of strong solutions to incompressible MHD
Pages: 1337  1345,
Issue 3,
May
2014
doi:10.3934/cpaa.2014.13.1337 Abstract
References
Full text (343.0K)
Related Articles
Huajun Gong  The Institute of Mathematical Sciences, University of Science and Technology of China, Anhui, 230026, China (email)
Jinkai Li  The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Hong Kong (email)
1 
A. G. Kulikovskiy and G. A. Lyubimov, Magnetohydrodynamics, Addison–Wesley, Reading, MA, 1965. 

2 
L. D. Landau and E. M. Lifchitz, Electrodynamics of Continuous Media, 2nd ed., Pergamon, New York, 1984. 

3 
M. Sermange and R. Temam, Some mathematical questions related to the MHD equations, Comm. Pure Appl. Math., 36 (1983), 635664. 

4 
G. Duvaut and J. L. Lions, Inequations en thermoelasticite et magnetohydrodynamique, Ach.Rational Mech. Anal., 46 (1972), 241279. 

5 
J. F. Gerbeau and C. Le Bris, Existence of solution for a densitydependent magnetohydrodynamic equation, Adv. Differential Equations, 2 (1997), 427452. 

6 
P. L. Lions, Mathematical Topics in Fluid Mechanics. Vol. 1. Incompressible Models, Oxford Lecture Series in Mathematics and its Applications, 3. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1996. 

7 
P. L. Lions, Mathematical topics in fluid mechanics. Vol. 2. Compressible models, Oxford Lecture Series in Mathematics and its Applications, 10. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1998. 

8 
X. P. Hu and D. H. Wang, Global existence and largetime behavior of solutions to the threedimensional equations of compressible Magnetohydrodynamic flows, Arch. Rational Mech. Anal., 197 (2010), 203238. 

9 
X. P. Hu and D. H. Wang, Global solutions to the threedimensional full compressible Magnetohydrodynamic flows, Commun. Math. Phys., 283 (2008), 255284. 

10 
J. S. Fan and W. H. Yu, Global variational solutions to the compressible magnetohydrodynamic equations, Nonlinear Analysis, 69 (2008), 36373660. 

11 
E. Feireisl, Dynamics of viscous compressible fluids, Oxford Lecture Series in Mathematics and its Applications, 26. Oxford University Press, Oxford, 2004. 

12 
E. Feireisl, A. Novotný and H. Petzeltová, On the existence of globally defined weak solutions to the NavierStokes equations, J. Math. Fluid Mech., 3 (2001), 358392. 

13 
B. Ducomet and E. Feireisl, The equation of Magnetohydrodynamics: on the interaction between matter and ration in the evolution of gaseous stars, Commun. Math. Phys., 266 (2006), 595629. 

14 
Q. Chen, Z. Tan and Y. J. Wang, Strong solutions to the incompressible magnetohydrodynamic equations, Math. Methods Appl. Sci., 34 (2011), 94107. 

15 
H. W. Wu, Strong solutions to the incompressible magnetohydrodynamic equations with vacuum, Comput. Math. Appl., 61 (2011), 27422753. 

16 
X. D. Huang and Y. Wang, Global strong solution to the 2D nonhomogeneous incompressible MHD system, J. Differential Equations, 254 (2013), 511527. 

17 
J. S. Fan and W. H. Yu, Strong solution to the compressible magnetohydrodynamic equations with vacuum, Nonlinear Anal. Real World Appl., 10 (2009), 392409. 

18 
X. L. Li, N. Su, and D. H. Wang, Local strong solution to the compressible magnetohydrodynamic flow with large data, J. Hyperbolic Differ. Equ., 8 (2011), 415436. 

19 
X. L. Li and D. H. Wang, Global strong solution to the threedimensional densitydependent incompressible magnetohydrodynamic flows, J. Differential Equations, 251 (2011), 15801615. 

20 
W. Von Wahl, Estimating $\nabla u$ by $\text{div} u$ and $\text{curl}u$, Math. Methods Appl. Sci., 15 (1992), 123143. 

21 
Y. Zhou, Remarks on regularities for the 3D MHD equations, Discrete Contin. Dyn. Syst., 12 (2005), 881886. 

22 
Y. Zhou, Regularity criteria for the 3D MHD equations in terms of the pressure, Internat. J. NonLinear Mech., 41 (2006), 11741180. 

23 
Y. Zhou, Regularity criteria for the generalized viscous MHD equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, 24 (2007), 491505. 

Go to top
