On the inviscid and non-resistive limit for the equations of incompressible magnetohydrodynamics

Mathematical Models and Methods in Applied Sciences

Volumn 12, Issue 10, 2002, Pages 1401-1419

  Diaz J I ^a   Lerena, M B ^b  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

Braginski viscosity operator; Incompressible viscous and ideal magnetohydrodynamics; Non resistive limit

Indexed keywords

EID: 0036812186     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202502002173     Document Type: Article

References (31)

1. R. Adams, Sobolev Spaces (Academic Press, 1975).
2. D. Biskamp, Nonlinear Magnetohydrodynamics (Cambridge Univ. Press, 1997).
3. S.I. Braginskii, in Transport Processes in a Plasma, Vol. 1, Reviews of a Plasma Physics (Consultants Bureau, 1965) pp. 205-311.
4. H. Brézis, Analyse Fonctionnelle (Masson Editeur, 1983).
5. R.E. Caflisch, I. Klapper and G. Steele, Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD, Commun. Math. Phys. 184 (1997) 443-455.
6. M. Cannone, Ondelettes, Paraproduits et Navier-Stokes, Nouveaux Essais (Diderot Ed., 1995).
7. T. Cazenave and A. Haraux, An Introduction to Semilinear Evolution Equations (Clarendon Press, 1998).
8. P. Constantin and C. Foias, Navier-Stokes Equations (The University of Chicago Press, 1988).
9. T.G. Cowling, Magnetohydrodynamics (John Wiley & Sons, 1965).
10. R. Dautray and J.L. Lions, Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques 9 (Masson, 1988).
11. J.I. Díaz, Simulación numérica de un Equilibrio de un Plasma Magnéticamente Confinado en un Stellarator, Informe #2, CIEMAT (1998).
12. G. Duvaut and J.L. Lions, Inéquations en thermoélasticité et magnétohydrodynamique, Arch. Rational Mech. Anal. 46 (1972) 241-279.
13. J.P. Freidberg, Ideal Magnetohydrodynamic Theory of Magnetic Fusion Systems, Rev. Moderm Physics Vol. 54, No. 3 (The American Physical Society, 1982).
14. D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order (Springer-Verlag, 1983).
15. R.D. Hazeltine and J.D. Meiss, Plasma Confinement (Addison-Wesley, 1992).
16. T. Kato, Quasi-linear equations of evolution, with applications to partial differential equations, Lect. Notes in Math., Vol. 448 (Springer-Verlag, 1975), pp. 25-70.
17. 3, J. Funct. Anal. 9 (1972) 296-305.
18. T. Kato, Perturbation Theory for Linear Operators (Springer, 1966).
19. T. Kato and G. Ponce, Commutator estimates and the Euler and Navier-Stokes equations, Comm. Pure and Appl. Math. XLI (1988) 891-907.
20. J. Rauch, Partial Differential Equations (Springer-Verlag, 1997).
21. P. Schmidt, On a magnetohydrodynamic problem of Euler type, J. Differrential Equation 74 (1988) 318-335.
22. P. Secchi, On the equations of ideal incompressible magneto-hydrodynamics, Rend. Sem. Ma. Univ. Padova 90 (1993) 104-119.
23. M. Spada and H. Wobig, On the existence and uniqueness of dissipative plasma equilibria in a toroidal domain, J. Phys. A: Math. Gen. 25 (1992) 1575-1591.
24. G. Ströhmer, About an initial-boundary value problem from magneto-hydrodynamics, Math. Z. 209 (1992) 345-362.
25. C. Sulem, Quelques résultats de régularité pour les équations de la MHD, C.R.A.S. Série A 285 (1977) 365-385.
26. 3, Trans. Amer. Math. Soc. 157 (1971) 373-397.
27. M.E. Taylor, Partial Differential Equations I: Basic Theory (Springer-Verlag, 1996).
28. M. Sermange and R. Temam, Some mathematical questions related to the MHD equations, Comm. Pure. Appl. Math. XXXVI (1983) 635-664.
29. R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis (North-Holland, 1979).
30. I. Vrabie, Semigrupuri de operatori liniari si aplicatii (Ed. "Universitatii Al. I. Cuza", Rumania, 2001).
31. J. Wu, Viscous and inviscid magneto-hydrodynamics equations, J. Anal. Math. 73 (1997) 251-265.