Geodesic
On the magnetohydrodynamic type equations in a new class of non-cylindrical domains
Bollettino della Unione matematica italiana, Série 8, 2B (1999) no. 2, pp. 365-382.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Viene provata l'esistenza e l'unicità delle soluzioni deboli per un sistema di equazioni della magnetoidrodinamica in un dominio variabile. Per la dimostrazione si usano il metodo di Galerkin spettrale e la tecnica introdotta da Dal Passo e Ughi per trattare i problemi con dominio dipendente dal tempo. 
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Berselli, Luigi C.; Ferreira, Jorge. On the magnetohydrodynamic type equations in a new class of non-cylindrical domains. Bollettino della Unione matematica italiana, Série 8, 2B (1999) no. 2, pp. 365-382. http://geodesic.mathdoc.fr/item/BUMI_1999_8_2B_2_a11/

[1] R. Adams , Sobolev Spaces., Academic Press (1975). | MR | Zbl

[2] A. C. Eringen - G. A. Maugin , Electrodynamics of Continua, volume 2, Springer, Berlin (1989).

[3] H. Fujita - N. Sauer , Construction of weak solutions of the navier-stokes equations in a non-cylindrical domain, Bull. Amer. Mat. Soc, 75 (1969), 465-468. | fulltext mini-dml | MR | Zbl

[4] G. Lassner , Über ein rand-anfangswert-problem der magnetohydrodinamik, Arch. Rational. Mech. Anal., 25 (1967), 388-405. | MR | Zbl

[5] J. D. Jackson , Classical Electrodynamics, 2 edition, J. Wiley and Sons Inc. (1975). | MR | Zbl

[6] J. L. Boldrini - M. A. Rojas-Medar , On a system of evolution equations of magnetohydrodynamic type, Mat. Contemp., 8 (1995), 1-19. | MR | Zbl

[7] J. L. Lions , Une remarque sur les problèmes d'evolution non linéaires dans des domains non cylindriques, Rev. Roumaine Math. Pures Appl., 9 (1964), 11-18. | MR | Zbl

[8] J. L. Lions , Quelque méthodes de résolution des problèmes aux limites non-lineaires, Dunod Gauthier-Villars (1969). | MR | Zbl

[9] O. A. Ladyzhenskaya , The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach (1969). | MR | Zbl

[10] J. Limaco , Navier-Stokes equations in non cylindrical domains, to appear.

[11] M. Rojas-Medar - R. Beltrán Barrios , The initial value problem for the equations of magnetohydrodynamic type in non-cylindrical domains, Rev. Mat. Un. Comp. Madrid, 8 (1995), 229-251. | MR | Zbl

[12] M. A. Rojas-Medar - J. L. Boldrini , Global strong solutions of equations of magnetohydrodynamic type, to appear. | MR | Zbl

[13] R. Dal Passo - M. Ughi , Problème de Dirichlet pour une classe d'équations paraboliques non linéaires dans des ouverts non cylindriques, C. R. Acad. Sci. Paris, 308 (1989), 555-558. | MR | Zbl

[14] Schlüter , Dynamic der plasmas I, II, Z. Naturforsch., 5a-6a (1950-51), 72-78, 73-79. | Zbl

[15] T. Kato - H. Fujita , On the Navier-Stokes initial value problem I., Arch. Rational. Mech. Anal., 16 (1964), 269-315. | MR | Zbl

[16] R. Temam , Navier-Stokes Equations. Theory and Numerical Analysis, 3rd edition, North-Holland (1984). | Zbl