On the equations of ideal incompressible magneto-hydrodynamics
Secchi, Paolo
Rendiconti del Seminario Matematico della Università di Padova, Tome 90 (1993), p. 103-119 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{RSMUP_1993__90__103_0,
     author = {Secchi, Paolo},
     title = {On the equations of ideal incompressible magneto-hydrodynamics},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {90},
     year = {1993},
     pages = {103-119},
     mrnumber = {1257135},
     zbl = {0808.35110},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_1993__90__103_0}
}

Secchi, Paolo. On the equations of ideal incompressible magneto-hydrodynamics. Rendiconti del Seminario Matematico della Università di Padova, Tome 90 (1993) pp. 103-119. http://gdmltest.u-ga.fr/item/RSMUP_1993__90__103_0/

[1] G.V. Alekseev, Solvability of a homogeneous initial-boundary value problem for equations of magnetohydrodynamics of an ideal fluid (Russian), Dinam. Sploshn. Sredy, 57 (1982), pp. 3-20. | MR 752597 | Zbl 0513.76106

[2] H. Beirão Da Veiga, Boundary-value problems for a class of first order partial differential equations in Sobolev spaces and applications to the Euler flow, Rend. Sem. Mat. Univ. Padova, 79 (1988), pp. 247-273. | Numdam | MR 964034 | Zbl 0709.35082

[3] H. Beirão Da Veiga, Kato's perturbation theory and well-posedness for the Euler equations in bounded domains, Arch. Rat. Mech. Anal., 104 (1988), pp. 367-382. | MR 960958 | Zbl 0672.35044

[4] H. Beirão Da Veiga, Existence results in Sobolev spaces for a stationary transport equations, Ric. Mat. Suppl., 36 (1987) pp. 173-184. | MR 956025 | Zbl 0691.35087

[5] H. Beirão Da Veiga, A well posedness theorem for non-homogeneous in-viscid fluids via a perturbation theorem, J. Diff. Eq., 78 (1989), pp. 308-319. | MR 992149 | Zbl 0682.35012

[6] H. Beirão Da Veiga - A. Valli, On the Euler equations for non-homogeneous fluids, (I) Rend. Sem. Mat. Univ. Padova, 63 (1980), 151-168; (II) J. Math. Anal. Appl., 73 (1980), pp. 338-350. | Numdam | Zbl 0459.76003

[7] H. Beirão Da Veiga - A. Valli, Existence of C∞ solutions of the Euler equations for non-homogeneous fluids, Commun. Partial Diff. Eq., 5 (1980), 95-107. | Zbl 0437.35059

[8] J.P. Freidberg, Ideal Magnetohydrohynamics, Plenum Press, New York-London (1987).

[9] D. Fujiwara - H. Morimoto, An Lr-theorem of the Helmholtz decomposition of vector fields, J. Fac. Sci. Univ. Tokyo, 24 (1977), pp. 685-700. | MR 492980 | Zbl 0386.35038

[10] T. Kato, Linear evolution equations of hyperbolic type, J. Fac. Sci. Univ. Tokyo, 17 (1970), pp. 241-258. | MR 279626 | Zbl 0222.47011

[11] T. Kato, Linear evolution equations of hyperbolic type II, J. Math. Soc. Japan, 25 (1973), pp. 648-666. | MR 326483 | Zbl 0262.34048

[12] T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Rat. Mech. Anal., 58 (1975), pp. 181-205. | MR 390516 | Zbl 0343.35056

[13] T. Kato - C. Y. LAI, Nonlinear evolution equations and the Euler flow, J. Funct. Analysis, 56 (1984), pp. 15-28. | MR 735703 | Zbl 0545.76007

[14] H. Kozono, Weak and classical solutions of the two-dimensional magnetohydrodynamics equations, Tohoku Math. J., 41 (1989), pp. 471-488. | MR 1007099 | Zbl 0683.76103

[15] J.E. Marsden, Well-posedness of the equations of a non-homogeneous perfect fluid, Commun. Partial Diff. Eq., 1 (1976), pp. 215-230. | MR 405493 | Zbl 0341.35019

[16] P.G. Schmidt, On a magnetohydrodynamic problem of Euler type, J. Diff. Eq., 74 (1988), pp. 318-335. | MR 952901 | Zbl 0675.35080

[17] P. Secchi, On an initial boundary value problem for the equations of ideal magnetohydrodynamics, to appear on Math. Meth. Appl. Sci. | MR 1346662 | Zbl 0838.35103

[18] R. Temam, On the Euler equations of incompressible perfect fluids, J. Funct. Anal., 20 (1975), pp. 32-43. | Zbl 0309.35061

[19] A. Valli - W. Zajaczkowski, About the motion of non-homogeneous ideal incompressible fluids, Non Linear Anal., 12 (1988), pp. 43-50. | MR 924751 | Zbl 0662.76037

[20] T. Yanagisawa - A. MATSUMURA, The fixed boundary value problems for the equations of ideal magneto-hydrodynamics with a perfectly conducting wall condition, Commun. Math. Phys., 136 (1991), pp. 119-140. | MR 1092572 | Zbl 0726.76111