The Weak solutions and reproductive property for a system of evolution equations of magnetohydrodynamic type
DOI:
https://doi.org/10.22199/S07160917.1994.0002.00002Keywords:
Galerkin, Fluidos eléctricosAbstract
By using the Galerkin method, we prove the existence of weak solutions for a system of equations of magnetohydrodynamic type. In the two-dimensional case, we prove that the weak solution is unique. We also prove the reproductive property and comment about the regularity of periodic solutions.
References
[1] Adams, R. A.: Sobolev Spaces, Academic Press, N.Y, 1975.
[2] Boldrini, J. L.; Rojas-Medar, M.A.: On a system of evolution equations of magnetohydrodynamic type: on the existence, regularity and approximations of solutions, Actas 2º Congreso de Matemática Capricornio, Arica, 23-28, 1992.
[3] Boldrini, J. L.; Rojas-Medar, M.A.: On a system of evolution equations of magnetohydrodynamic type, to appear in Mat. Contemp.
[4] Chizhonkov, E. V.: On a system of equation of magnetohydrodynamic type, Soviet Math. Dokl. 30, 542-545, 1984.
[5] Fujita, H. and Kato, T.: On the Navier-Stokes initial value problem, I, Arch.Rational Mech. Anal., 16 (1964), 269-315.
[6] Kaniel, S.; Shinbrot, M.: A reproductive property of the Navier-Stokes equations, Arch. Rational Mech. Anakl. 24, 363-369, 1967.
[7] Lassner, G.: Über ein randanfargswert problem der mangnetohydrodynamik, Arch. Rational Mech. Anal, 25, 388-405, 1967.
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[9] Pikelner, S. B.: Grundlagen der Kosmischen elektrodynamik, Moscou, 1966.
[10] Rojas-Medar, M. A.; Boldrini, J.L.: Global strong solutions of the equations of magnetohydrodynamic type, Research Report 1993/53, IMECC-UNICAMP, Brasil, 1993, submitted.
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[2] Boldrini, J. L.; Rojas-Medar, M.A.: On a system of evolution equations of magnetohydrodynamic type: on the existence, regularity and approximations of solutions, Actas 2º Congreso de Matemática Capricornio, Arica, 23-28, 1992.
[3] Boldrini, J. L.; Rojas-Medar, M.A.: On a system of evolution equations of magnetohydrodynamic type, to appear in Mat. Contemp.
[4] Chizhonkov, E. V.: On a system of equation of magnetohydrodynamic type, Soviet Math. Dokl. 30, 542-545, 1984.
[5] Fujita, H. and Kato, T.: On the Navier-Stokes initial value problem, I, Arch.Rational Mech. Anal., 16 (1964), 269-315.
[6] Kaniel, S.; Shinbrot, M.: A reproductive property of the Navier-Stokes equations, Arch. Rational Mech. Anakl. 24, 363-369, 1967.
[7] Lassner, G.: Über ein randanfargswert problem der mangnetohydrodynamik, Arch. Rational Mech. Anal, 25, 388-405, 1967.
[8] Lions, J. L.: Quelques méthodes de résolution des problémes aux limites nonlinéares, Dunod Gauthier-Villars, Paris, 1969.
[9] Pikelner, S. B.: Grundlagen der Kosmischen elektrodynamik, Moscou, 1966.
[10] Rojas-Medar, M. A.; Boldrini, J.L.: Global strong solutions of the equations of magnetohydrodynamic type, Research Report 1993/53, IMECC-UNICAMP, Brasil, 1993, submitted.
[11] Schlüter, A.: Dynamik des plasmas, I and II, Z. Naturforsch. 5a, 72-78, 1950; 6a, 73-79, 1951.
[12] Temam, R.: Navier-Stokes Equations, North-Holland, Amsterdam, Rev. Edit., 1979.
Published
2018-04-03
How to Cite
[1]
M. A. Rojas Medar and J. L. Boldrini, “The Weak solutions and reproductive property for a system of evolution equations of magnetohydrodynamic type”, Proyecciones (Antofagasta, On line), vol. 13, no. 2, pp. 85-97, Apr. 2018.
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