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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 402793, 6 pages
Notes on the Global Well-Posedness for the Maxwell-Navier-Stokes System
1Department of Mathematics, Chosun University, Gwangju 501-759, Republic of Korea
2Department of Mathematics, Chung-Ang University, Seoul 156-756, Republic of Korea
Received 28 March 2013; Accepted 26 June 2013
Academic Editor: Changxing Miao
Copyright © 2013 Ensil Kang and Jihoon Lee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- P. Germain, S. Ibrahim, and N. Masmoudi, “On the wellposedness of the Navier-Stokes-Maxwell system,” http://arxiv.org/abs/1207.6187.
- N. Masmoudi, “Global well posedness for the Maxwell-Navier-Stokes system in 2D,” Journal de Mathématiques Pures et Appliquées. Neuvième Série, vol. 93, no. 6, pp. 559–571, 2010.
- D. D'Ambrosio and D. Giordano, “Electromagnetic fluid dynamics for aerospace applications. Part I: classification and critical review of physical models,” in Proceedings of the 35th AIAA Plasmadynamics and Lasers Conference, Portland, Ore, USA, June 2004, AIAA Paper 2004-2165.
- D. D'Ambrosio, M. Pandol, and D. Giordano, “Electromagnetic fluid dynamics for aerospace applications. Part II: numerical simulations using different physical models,” in Proceedings of the 35th AIAA Plasmadynamics and Lasers Conference, Portland, Ore, USA, June 2004, AIAA Paper 2004-2362.
- P. A. Davidson, An Introduction to Magnetohydrodynamics, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, UK, 2001.
- C. Cao and J. Wu, “Two regularity criteria for the 3D MHD equations,” Journal of Differential Equations, vol. 248, no. 9, pp. 2263–2274, 2010.
- C. Cao and J. Wu, “Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion,” Advances in Mathematics, vol. 226, no. 2, pp. 1803–1822, 2011.
- G. Duvaut and J.-L. Lions, “Inéquations en thermoélasticité et magnétohydrodynamique,” Archive for Rational Mechanics and Analysis, vol. 46, pp. 241–279, 1972.
- Z. Lei and Y. Zhou, “BKM's criterion and global weak solutions for magnetohydrodynamics with zero viscosity,” Discrete and Continuous Dynamical Systems. Series A, vol. 25, no. 2, pp. 575–583, 2009.
- M. Sermange and R. Temam, “Some mathematical questions related to the MHD equations,” Communications on Pure and Applied Mathematics, vol. 36, no. 5, pp. 635–664, 1983.
- J. Wu, “Regularity criteria for the generalized MHD equations,” Communications in Partial Differential Equations, vol. 33, no. 1–3, pp. 285–306, 2008.
- Y. Zhou, “Regularity criteria for the generalized viscous MHD equations,” Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, vol. 24, no. 3, pp. 491–505, 2007.
- J.-Y. Chemin and N. Lerner, “Flot de champs de vecteurs non lipschitziens et équations de Navier-Stokes,” Journal of Differential Equations, vol. 121, no. 2, pp. 314–328, 1995.
- S. Ibrahim and S. Keraani, “Global small solutions for the Navier-Stokes-Maxwell system,” SIAM Journal on Mathematical Analysis, vol. 43, no. 5, pp. 2275–2295, 2011.
- R. Duan, “Green's function and large time behavior of the Navier-Stokes-Maxwell system,” Analysis and Applications, vol. 10, no. 2, pp. 133–197, 2012.
- S. Ibrahim and T. Yoneda, “Local solvability and loss of smoothness of the Navier-Stokes-Maxwell equations with large initial data,” Journal of Mathematical Analysis and Applications, vol. 396, no. 2, pp. 555–561, 2012.
- P. Germain and N. Masmoudi, “Global existence for the Euler-Maxwell system,” http://arxiv.org/abs/1107.1595.
- J. Jang and N. Masmoudi, “Derivation of Ohm's law from the kinetic equations,” SIAM Journal on Mathematical Analysis, vol. 44, no. 5, pp. 3649–3669, 2012.
- D. Chae, “Global regularity for the 2D Boussinesq equations with partial viscosity terms,” Advances in Mathematics, vol. 203, no. 2, pp. 497–513, 2006.
- A. J. Majda and A. L. Bertozzi, Vorticity and Incompressible Flow, vol. 27 of Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, UK, 2002.