On a system of evolution equations of magnetohydrodynamic type: an iterational approach


  • E. A. Notte-Cuello Universidad de Antofagasta.
  • M. A. Rojas-Medar Universidad Estadual de Campinas.




In this work we present a new proof of the existence and uniqueness of strong solution for the magnetohydrodynamic type equations. We use an iterational approach and we give the convergence-rates for this method.

Author Biographies

E. A. Notte-Cuello, Universidad de Antofagasta.

Departamento de Matemáticas.


M. A. Rojas-Medar, Universidad Estadual de Campinas.

DMA - Instituto de Matemáticas, Estatística e Ciencia da Computacao.


[1] Amrouche, G. and Girault, V., On the existence and regularity of the solutions of Stokes problem in arbitrary dimension, Proc. Japan Acad., 67, Ser. A. (1991), 171-175.

[2] Boldrini, J.L. And Rojas-Medar, M.A., On a system of evolution equations of Magnetohydrodinamic type, Mat. Cont., 8, 1-19, 1995.

[3] Constantin, P. and Foias C., Navier-Stokes equations, The Univ. Chicago Press, Chicago and London, 1988.

[4] Damásio, P. and Rojas-Medar, M.A., On some questions of the weak solutions of evolution equations for magnetohydrodynamic type, Proyecciones 16(1997), 83-97 ..

[5] Fujita, H. and Kato, T., On the Navier-Stokes initial value problem I, Arch. Rat. Mech. Anal. 16(1964), 269-315.

[6] Lassner, G., Über Ein Rand-Anfangswert - Problem der Magnetohydrodinamik, Arch. Rat. Mech. Anal. 25 (1967), 388-405.

[7] Lions, J.L., Quelques Methods de Resolution des Problémes aux Limits Non Linéares, Dunod, París, 1969.

[8] Pikelner, S.B., Grundlangen der Kosmischen Elektrohydrodynamik, Moscou, 1966.

[9] Rojas-Medar, M.A. and Beltrán-Barrios, R., The initial value problem for the equations of magnetohydrodynamic type in noncylindrical domains, Rev. Mat. Univ. Compl. Madrid, 8 (1995), 229-251.

[10] Rojas-Medar, M.A. and Boldrini, J.L. Global strong solutions of equations of magnetohydrodynamic type, J. Australian Math. Soc., Serie B, Applied Math 38 (1997), 291-306.

[11] Schlüter, A., Dynamic des Plasmas, I and II. Z. Naturforsch. 5a (1950), 72-78; 6a, (1951), 73-79.

[12] Sedov, V.I. and Fokht, A.S., Correctness of Fitz Hugh's problern, Diff. Urav. 16 (1980), 114-1121.

[13] Temam, R., Navier-Stokes equations, North-Holland, Amsterdam, Rev. Edit., 1979.

[14] Zarubin, A.G., On an iterational method for the approximate solution of an initial - and boundary-value problem for the heat-convection equations, Comput. Math. Phys. 33 (1993), 1077-1085.



How to Cite

E. A. Notte-Cuello and M. A. Rojas-Medar, “On a system of evolution equations of magnetohydrodynamic type: an iterational approach”, Proyecciones (Antofagasta, On line), vol. 17, no. 2, pp. 133-165, Apr. 2018.