A global existence result in Sobolev spaces for MHD system in the half-plane
Rendiconti del Seminario Matematico della Università di Padova, Volume 108 (2002), p. 79-91
@article{RSMUP_2002__108__79_0,
     author = {Casella, Emanuela and Trebeschi, Paola},
     title = {A global existence result in Sobolev spaces for MHD system in the half-plane},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {108},
     year = {2002},
     pages = {79-91},
     zbl = {1058.35175},
     mrnumber = {1956431},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2002__108__79_0}
}
Casella, Emanuela; Trebeschi, Paola. A global existence result in Sobolev spaces for MHD system in the half-plane. Rendiconti del Seminario Matematico della Università di Padova, Volume 108 (2002) pp. 79-91. http://www.numdam.org/item/RSMUP_2002__108__79_0/

[1] G. V. Alexseev, 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, A well posedness theorem for non-homogeneous inviscid fluids via a perturbation theorem, (II) J. Diff. Eq., 78 (1989), pp. 308-319. | MR 992149 | Zbl 0682.35012

[5] E. Casella - P. Secchi - P. Trebeschi, Global classical solutions for MHD system, to appear on Journal of Math. Fluid Mech., Mathematic. | MR 1966645 | Zbl 1037.76068

[6] T. Kato, On Classical Solutions of Two-Dimensional Non-Stationary Euler Equation, Arch. Rat. Mech. Anal., 25 (1967), pp. 188-200. | MR 211057 | Zbl 0166.45302

[7] 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

[8] K. Kikuchi, Exterior problem for the two-dimensional Euler equation, J. Fac. Sci. Univ. Tokyo, Sec IA 30 (1983), pp. 63-92. | MR 700596 | Zbl 0517.76024

[9] H. Kozono, Weak and Classical Solutions of the Two-dimensional magnetohydrodynamic equations, Tohoku Math. J., 41 (1989), pp. 471-488. | MR 1007099 | Zbl 0683.76103

[10] L. Lichtenstein, Grundlagen der Hydromechanik, Edition of 1928 Springer, Berlin, 1968. | JFM 55.1124.01 | MR 228225 | Zbl 0157.56701

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

[12] P. Secchi, On the Equations of Ideal Incompressible Magneto-Hydrodynamics, Rend. Sem. Mat. Univ. Padova, 90 (1993), pp. 103-119. | Numdam | MR 1257135 | Zbl 0808.35110

[13] R. Temam, Navier-Stokes Equations, 2nd Ed., North-Holland, Amsterdam, 1979. | MR 603444 | Zbl 0426.35003

[14] R. Temam, On the Euler equations of incompressible perfect fluids, J. Funct. Anal., 20 (1975), pp. 32-43. | MR 430568 | Zbl 0309.35061

[15] W. Wolibner, Un théorèm sur l'existence du mouvement plan d'un fluide parfait, homogène, incompressible, pendant un temps infiniment longue, Math. Z., 37 (1933), pp. 698-726. | MR 1545430 | Zbl 0008.06901