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On the global well-posedness to the 3-D incompressible anisotropic magnetohydrodynamics equations
On the global well-posedness to the 3-D Navier-Stokes-Maxwell system
1. | Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106 |
2. | Department of Mathematics, Nanjing University, Nanjing 210093 |
References:
[1] |
H. Bahouri, J. Chemin and R. Danchin, Fourier Analysis and Nonlinear Partial Differential Equations, Springer, 2011.
doi: 10.1007/978-3-642-16830-7. |
[2] |
J. Chemin, Localization in Fourier space and Navier-Stokes system Phase space analysis of Partial Differential Equations, Pubbl. Cert. Ric. Mat. Ennio de Gorg Scuola Norma. Sup. Pisa, \textbfI (2004), 53-135. |
[3] |
J. Chemin and N. Lerner, Flot de champs de vecteurs non lipschitziens et équations de Navier-Stokes, J. Differential Equations, 121 (1995), 314-328.
doi: 10.1006/jdeq.1995.1131. |
[4] |
J. Chemin and P. Zhang, On the global wellposedness to the 3-D incompressible anisotropic Navier-Stokes equations, Commun. Math. Phys., 272 (2007), 529-566.
doi: 10.1007/s00220-007-0236-0. |
[5] |
R. Danchin, Local theory in critical spaces for compressible viscous and heat-conducting gases, Comm. Partial Differential Equations, 26 (2001), 1183-1233.
doi: 10.1081/PDE-100106132. |
[6] |
P. Davidson, An Introduction to Magnetohydrodynamics, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2001.
doi: 10.1017/CBO9780511626333. |
[7] |
P. Germain, S. Ibrahim and N. Masmoudi, Well-posedness of the Navier-Stokes-Maxwell equations, Proceedings of the Royal Society of Edinburgh, 144 (2014), 71-86.
doi: 10.1017/S0308210512001242. |
[8] |
G. Gui and P. Zhang, Stability to the global large solutions of 3-D Navier-Stokes equations, Adv. Math., 225 (2010), 1248-1284.
doi: 10.1016/j.aim.2010.03.022. |
[9] |
S. Ibrahim and S. Keraani, Global small solutions for the coupled Navier-Maxwell system, SIAM J. Math. Anal., 43 (2011), 2275-2295.
doi: 10.1137/100819813. |
[10] |
S. Ibrahim and T. Yoneda, Local solvability and loss of smoothness of the Navier-Stokes- Maxwell equations with large initial data, J. Math. Analysis Applic., 396 (2012), 555-561.
doi: 10.1016/j.jmaa.2012.06.038. |
[11] |
N. Masmoudi, Global well posedness for the Maxwell-Navier-Stokes system in 2D, J. Math. Pures Appl., 93 (2010), 559-571.
doi: 10.1016/j.matpur.2009.08.007. |
[12] |
M. Paicu and P. Zhang, Global solutions to the 3-D incompressible anisotropic Navier-Stokes system in the critical spaces, Comm. Math. Phys., 307 (2011), 713-759.
doi: 10.1007/s00220-011-1350-6. |
[13] |
M. Paicu and P. Zhang, Global solutions to the 3-D incompressible inhomogeneous Navier-Stokes system, J. Funct. Anal., 262 (2012), 3556-3584.
doi: 10.1016/j.jfa.2012.01.022. |
[14] |
T. Zhang, Global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations in an anisotropic space, Commun. Math. Phys., 287 (2009), 211-224.
doi: 10.1007/s00220-008-0631-1. |
show all references
References:
[1] |
H. Bahouri, J. Chemin and R. Danchin, Fourier Analysis and Nonlinear Partial Differential Equations, Springer, 2011.
doi: 10.1007/978-3-642-16830-7. |
[2] |
J. Chemin, Localization in Fourier space and Navier-Stokes system Phase space analysis of Partial Differential Equations, Pubbl. Cert. Ric. Mat. Ennio de Gorg Scuola Norma. Sup. Pisa, \textbfI (2004), 53-135. |
[3] |
J. Chemin and N. Lerner, Flot de champs de vecteurs non lipschitziens et équations de Navier-Stokes, J. Differential Equations, 121 (1995), 314-328.
doi: 10.1006/jdeq.1995.1131. |
[4] |
J. Chemin and P. Zhang, On the global wellposedness to the 3-D incompressible anisotropic Navier-Stokes equations, Commun. Math. Phys., 272 (2007), 529-566.
doi: 10.1007/s00220-007-0236-0. |
[5] |
R. Danchin, Local theory in critical spaces for compressible viscous and heat-conducting gases, Comm. Partial Differential Equations, 26 (2001), 1183-1233.
doi: 10.1081/PDE-100106132. |
[6] |
P. Davidson, An Introduction to Magnetohydrodynamics, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2001.
doi: 10.1017/CBO9780511626333. |
[7] |
P. Germain, S. Ibrahim and N. Masmoudi, Well-posedness of the Navier-Stokes-Maxwell equations, Proceedings of the Royal Society of Edinburgh, 144 (2014), 71-86.
doi: 10.1017/S0308210512001242. |
[8] |
G. Gui and P. Zhang, Stability to the global large solutions of 3-D Navier-Stokes equations, Adv. Math., 225 (2010), 1248-1284.
doi: 10.1016/j.aim.2010.03.022. |
[9] |
S. Ibrahim and S. Keraani, Global small solutions for the coupled Navier-Maxwell system, SIAM J. Math. Anal., 43 (2011), 2275-2295.
doi: 10.1137/100819813. |
[10] |
S. Ibrahim and T. Yoneda, Local solvability and loss of smoothness of the Navier-Stokes- Maxwell equations with large initial data, J. Math. Analysis Applic., 396 (2012), 555-561.
doi: 10.1016/j.jmaa.2012.06.038. |
[11] |
N. Masmoudi, Global well posedness for the Maxwell-Navier-Stokes system in 2D, J. Math. Pures Appl., 93 (2010), 559-571.
doi: 10.1016/j.matpur.2009.08.007. |
[12] |
M. Paicu and P. Zhang, Global solutions to the 3-D incompressible anisotropic Navier-Stokes system in the critical spaces, Comm. Math. Phys., 307 (2011), 713-759.
doi: 10.1007/s00220-011-1350-6. |
[13] |
M. Paicu and P. Zhang, Global solutions to the 3-D incompressible inhomogeneous Navier-Stokes system, J. Funct. Anal., 262 (2012), 3556-3584.
doi: 10.1016/j.jfa.2012.01.022. |
[14] |
T. Zhang, Global wellposed problem for the 3-D incompressible anisotropic Navier-Stokes equations in an anisotropic space, Commun. Math. Phys., 287 (2009), 211-224.
doi: 10.1007/s00220-008-0631-1. |
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