Shear layer solutions of incompressible MHD and dynamo effect
Gérard-Varet, David ; Rousset, Frédéric
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007), p. 677-710 / Harvested from Numdam
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@article{AIHPC_2007__24_5_677_0,
     author = {G\'erard-Varet, David and Rousset, Fr\'ed\'eric},
     title = {Shear layer solutions of incompressible MHD and dynamo effect},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {24},
     year = {2007},
     pages = {677-710},
     doi = {10.1016/j.anihpc.2006.04.005},
     mrnumber = {2348048},
     zbl = {1128.76066},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2007__24_5_677_0}
}

Gérard-Varet, David; Rousset, Frédéric. Shear layer solutions of incompressible MHD and dynamo effect. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) pp. 677-710. doi : 10.1016/j.anihpc.2006.04.005. http://gdmltest.u-ga.fr/item/AIHPC_2007__24_5_677_0/

[1] Chossat P., Iooss G., The Couette-Taylor Problem, Applied Mathematical Sciences, vol. 102, Springer-Verlag, New York, 1994. | Zbl 0817.76001

[2] Desjardins B., Grenier E., Linear instability implies nonlinear instability for various types of viscous boundary layers, Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (1) (2003) 87-106. | Numdam | MR 1958163 | Zbl 1114.76024

[3] Fearn D., Hydromagnetic flows in planetary cores, Rep. Prog. Phys. 61 (1998) 175-235.

[4] Gailitis A., Lielausis O., Platacis E., Gerbeth G., Stefani F., Riga dynamo experiment and its theoretical background, Phys. Plasmas 11 (5) (2004) 2838-2843. | MR 2062703

[5] Gérard-Varet D., Oscillating solutions of incompressible MHD and dynamo effect, SIAM J. Math. Anal. 37 (3) (2005) 815-840. | MR 2191778 | Zbl pre05029358

[6] Gilbert A.D., Fast dynamo action in the Ponomarenko dynamo, Geophys. Astrophys. Fluid Dynamics 44 (1988) 241-258. | Zbl 0676.76096

[7] Gilbert A.D., Dynamo theory, in: Handbook of Mathematical Fluid Dynamics, vol. II, North-Holland, Amsterdam, 2003, pp. 355-441. | MR 1984156 | Zbl 1033.76061

[8] Goodman J., Xin Z.P., Viscous limits for piecewise smooth solutions to systems of conservation laws, Arch. Rational Mech. Anal. 121 (3) (1992) 235-265. | MR 1188982 | Zbl 0792.35115

[9] Grenier E., On the nonlinear instability of Euler and Prandtl equations, Comm. Pure Appl. Math. 53 (9) (2000) 1067-1091. | MR 1761409 | Zbl 1048.35081

[10] Henry D., Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin, 1981. | MR 610244 | Zbl 0456.35001

[11] Ponomarenko Y., On the theory of hydromagnetic dynamos, Zh. Prikl. Mekh. Tekh. Fiz. (USSR) 44 (1973) 47-51.

[12] Roberts P., An Introduction to Magnetohydrodynamics, Longmans, Green, 1967.