Abstract
A magnetohydrodynamic system is investigated in
both cases of the periodic domain
A magnetohydrodynamic system is investigated in
both cases of the periodic domain
A. Babin, A. Mahalov, and B. Nicolaenko, “Global splitting, integrability and regularity of D Euler and Navier-Stokes equations for uniformly rotating fluids,” European Journal of Mechanics. B Fluids, vol. 15, no. 3, pp. 291–300, 1996.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. Benameur, M. Ghazel, and M. Majdoub, “About MHD system with small parameter,” Asymptotic Analysis, vol. 41, no. 1, pp. 1–21, 2005.
View at: Google Scholar | MathSciNetJ. Benameur, S. Ibrahim, and M. Majdoub, “Asymptotic study of a magneto-hydrodynamic system,” Differential and Integral Equations, vol. 18, no. 3, pp. 299–324, 2005.
View at: Google Scholar | MathSciNetJ.-Y. Chemin, “About Navier-Stokes Equations,” Publication du Laboratoire Jacques-Louis Lions, Université de Paris VI, R96023, 1996.
View at: Google ScholarJ.-Y. Chemin, B. Desjardins, I. Gallagher, and E. Grenier, “Fluids with anisotropic viscosity,” M2AN. Mathematical Modelling and Numerical Analysis, vol. 34, no. 2, pp. 315–335, 2000.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ.-Y. Chemin, B. Desjardins, I. Gallagher, and E. Grenier, “Anisotropy and dispersion in rotating fluids,” in Nonlinear Partial Differential Equations and Their Applications. Collège de France Seminar, Vol. XIV (Paris, 1997/1998), vol. 31 of Studies in Mathematics and Its Applications, pp. 171–192, North-Holland, Amsterdam, 2002.
View at: Google Scholar | Zentralblatt MATH | MathSciNetB. Desjardins, E. Dormy, and E. Grenier, “Stability of mixed Ekman-Hartmann boundary layers,” Nonlinearity, vol. 12, no. 2, pp. 181–199, 1999.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetE. Dormy, Modélisation numérique de la dynamo terrestre, Thèse de Doctorat, Institut de Physique du Globe de Paris, Paris, 1997.
View at: Google ScholarI. Gallagher, “Applications of Schochet's methods to parabolic equations,” Journal de Mathématiques Pures et Appliquées. Neuvième Série, vol. 77, no. 10, pp. 989–1054, 1998.
View at: Google Scholar | MathSciNetI. Gallagher, “Asymptotic of the solutions of hyperbolic equations with a skew-symmetric perturbation,” Journal of Differential Equations, vol. 150, no. 2, pp. 363–384, 1998.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetE. Grenier, “Oscillatory perturbations of the Navier-Stokes equations,” Journal de Mathématiques Pures et Appliquées. Neuvième Série, vol. 76, no. 6, pp. 477–498, 1997.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ.-L. Joly, G. Métivier, and J. Rauch, “Generic rigorous asymptotic expansions for weakly nonlinear multidimensional oscillatory waves,” Duke Mathematical Journal, vol. 70, no. 2, pp. 373–404, 1993.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ.-L. Joly, G. Métivier, and J. Rauch, “Coherent and focusing multidimensional nonlinear geometric optics,” Annales Scientifiques de l'École Normale Supérieure. Quatrième Série, vol. 28, no. 1, pp. 51–113, 1995.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. Klainerman and A. Majda, “Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids,” Communications on Pure and Applied Mathematics, vol. 34, no. 4, pp. 481–524, 1981.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, vol. 53 of Applied Mathematical Sciences, Springer, New York, 1984.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM.-G. Paicu, “Étude asymptotique pour les fluides anisotropes en rotation rapide dans le cas périodique,” Journal de Mathématiques Pures et Appliquées. Neuvième Série, vol. 83, no. 2, pp. 163–242, 2004.
View at: Google Scholar | MathSciNetS. Schochet, “The compressible Euler equations in a bounded domain: existence of solutions and the incompressible limit,” Communications in Mathematical Physics, vol. 104, no. 1, pp. 49–75, 1986.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. Schochet, “Fast singular limits of hyperbolic PDEs,” Journal of Differential Equations, vol. 114, no. 2, pp. 476–512, 1994.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetR. Temam, Navier-Stokes Equations, vol. 2 of Studies in Mathematics and Its Applications, North-Holland, Amsterdam, 1984.
View at: Google Scholar | Zentralblatt MATH | MathSciNet