On the magnetohydrodynamic type equations in a new class of non-cylindrical domains
Berselli, Luigi C. ; Ferreira, Jorge
Bollettino dell'Unione Matematica Italiana, Tome 2-A (1999), p. 365-382 / Harvested from 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.

Publié le : 1999-06-01
@article{BUMI_1999_8_2B_2_365_0,
     author = {Luigi C. Berselli and Jorge Ferreira},
     title = {On the magnetohydrodynamic type equations in a new class of non-cylindrical domains},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {2-A},
     year = {1999},
     pages = {365-382},
     zbl = {0942.76087},
     mrnumber = {1706576},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_1999_8_2B_2_365_0}
}
Berselli, Luigi C.; Ferreira, Jorge. On the magnetohydrodynamic type equations in a new class of non-cylindrical domains. Bollettino dell'Unione Matematica Italiana, Tome 2-A (1999) pp. 365-382. http://gdmltest.u-ga.fr/item/BUMI_1999_8_2B_2_365_0/

[1] Adams, R., Sobolev Spaces., Academic Press (1975). | MR 450957 | Zbl 0314.46030

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

[3] Fujita, H.-Sauer, N., Construction of weak solutions of the navier-stokes equations in a non-cylindrical domain, Bull. Amer. Mat. Soc, 75 (1969), 465-468. | MR 239290 | Zbl 0194.41401

[4] Lassner, G., Über ein rand-anfangswert-problem der magnetohydrodinamik, Arch. Rational. Mech. Anal., 25 (1967), 388-405. | MR 216809 | Zbl 0152.45502

[5] Jackson, J. D., Classical Electrodynamics, 2 edition, J. Wiley and Sons Inc. (1975). | MR 436782 | Zbl 0114.42903

[6] Boldrini, J. L.-Rojas-Medar, M. A., On a system of evolution equations of magnetohydrodynamic type, Mat. Contemp., 8 (1995), 1-19. | MR 1330029 | Zbl 0854.35087

[7] Lions, J. L., Une remarque sur les problèmes d'evolution non linéaires dans des domains non cylindriques, Rev. Roumaine Math. Pures Appl., 9 (1964), 11-18. | MR 213715 | Zbl 0178.12302

[8] Lions, J. L., Quelque méthodes de résolution des problèmes aux limites non-lineaires, Dunod Gauthier-Villars (1969). | MR 259693 | Zbl 0189.40603

[9] Ladyzhenskaya, O. A., The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach (1969). | MR 254401 | Zbl 0184.52603

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

[11] Rojas-Medar, M.-Beltrán Barrios, R., The initial value problem for the equations of magnetohydrodynamic type in non-cylindrical domains, Rev. Mat. Un. Comp. Madrid, 8 (1995), 229-251. | MR 1356444 | Zbl 0844.35094

[12] Rojas-Medar, M. A.-Boldrini, J. L., Global strong solutions of equations of magnetohydrodynamic type, to appear. | MR 1437958 | Zbl 0888.35086

[13] Dal Passo, R.-Ughi, M., 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 999454 | Zbl 0696.35088

[14] Schlüter, , Dynamic der plasmas I, II, Z. Naturforsch., 5a-6a (1950-51), 72-78, 73-79. | Zbl 0042.22404

[15] Kato, T.-Fujita, H., On the Navier-Stokes initial value problem I., Arch. Rational. Mech. Anal., 16 (1964), 269-315. | MR 166499 | Zbl 0126.42301

[16] Temam, R., Navier-Stokes Equations. Theory and Numerical Analysis, 3rd edition, North-Holland (1984). | Zbl 0568.35002