On the equations of ideal incompressible magneto-hydrodynamics

Paolo Secchi

Rendiconti del Seminario Matematico della Università di Padova (1993)

  • Volume: 90, page 103-119
  • ISSN: 0041-8994

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Secchi, Paolo. "On the equations of ideal incompressible magneto-hydrodynamics." Rendiconti del Seminario Matematico della Università di Padova 90 (1993): 103-119. <http://eudml.org/doc/108297>.

@article{Secchi1993,
author = {Secchi, Paolo},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {existence; uniqueness},
language = {eng},
pages = {103-119},
publisher = {Seminario Matematico of the University of Padua},
title = {On the equations of ideal incompressible magneto-hydrodynamics},
url = {http://eudml.org/doc/108297},
volume = {90},
year = {1993},
}

TY - JOUR
AU - Secchi, Paolo
TI - On the equations of ideal incompressible magneto-hydrodynamics
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1993
PB - Seminario Matematico of the University of Padua
VL - 90
SP - 103
EP - 119
LA - eng
KW - existence; uniqueness
UR - http://eudml.org/doc/108297
ER -

References

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  2. [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. Zbl0709.35082MR964034
  3. [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. Zbl0672.35044MR960958
  4. [4] H. Beirão Da Veiga, Existence results in Sobolev spaces for a stationary transport equations, Ric. Mat. Suppl., 36 (1987) pp. 173-184. Zbl0691.35087MR956025
  5. [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. Zbl0682.35012MR992149
  6. [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. Zbl0459.76003
  7. [7] H. Beirão Da Veiga - A. Valli, Existence of C∞ solutions of the Euler equations for non-homogeneous fluids, Commun. PartialDiff. Eq., 5 (1980), 95-107. Zbl0437.35059
  8. [8] J.P. Freidberg, Ideal Magnetohydrohynamics, Plenum Press, New York-London (1987). 
  9. [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. Zbl0386.35038MR492980
  10. [10] T. Kato, Linear evolution equations of hyperbolic type, J. Fac. Sci. Univ. Tokyo, 17 (1970), pp. 241-258. Zbl0222.47011MR279626
  11. [11] T. Kato, Linear evolution equations of hyperbolic type II, J. Math. Soc. Japan, 25 (1973), pp. 648-666. Zbl0262.34048MR326483
  12. [12] T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Rat. Mech. Anal., 58 (1975), pp. 181-205. Zbl0343.35056MR390516
  13. [13] T. Kato - C. Y. LAI, Nonlinear evolution equations and the Euler flow, J. Funct. Analysis, 56 (1984), pp. 15-28. Zbl0545.76007MR735703
  14. [14] H. Kozono, Weak and classical solutions of the two-dimensional magnetohydrodynamics equations, Tohoku Math. J., 41 (1989), pp. 471-488. Zbl0683.76103MR1007099
  15. [15] J.E. Marsden, Well-posedness of the equations of a non-homogeneous perfect fluid, Commun. PartialDiff. Eq., 1 (1976), pp. 215-230. Zbl0341.35019MR405493
  16. [16] P.G. Schmidt, On a magnetohydrodynamic problem of Euler type, J. Diff. Eq., 74 (1988), pp. 318-335. Zbl0675.35080MR952901
  17. [17] P. Secchi, On an initial boundary value problem for the equations of ideal magnetohydrodynamics, to appear on Math. Meth. Appl. Sci. Zbl0838.35103MR1346662
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