On the linear force-free fields in bounded and unbounded three-dimensional domains
ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 2, pp. 359-393. 
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Boulmezaoud, Tahar-Zamène; Maday, Yvon; Amari, Tahar. On the linear force-free fields in bounded and unbounded three-dimensional domains. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 2, pp. 359-393. http://www.numdam.org/item/M2AN_1999__33_2_359_0/

[1] S. Agmon, On the eigenfuntions and on the eigenvalnes of general elliptic boundary value problems. Comm. Pure Appl. Math.15 (1962) 119-147. | MR | Zbl

[2] C. E. Allissandrakis, On the computation of constant α force-free fields. Astron. Astrophys. 100 (1981) 197-200.

[3] J. J. Aly, A model for magnetic storage and Taylor's relaxation in the solar corona: I. Helicity-constrained minimum energy state in a half-cylinder, Phys. Fluids B 5 (1993) 151-163. | MR

[4] J. J. Aly, On some properties of force-free magnetic fields in infinite regions of space. Astrophys. J. 283 (1984) 349-362.

[5] T. Amari, J.J. Aly, J.F. Luciani, T. Z. Boulmezaoud and Z. Mikic, Reconstructing the solar coronal magnetic field as a force free magnetic field. Solar Physics 174 (1997) 129-149.

[6] P. R. Baldwin and G. M. Townsend, Complex Trkalian fields and solutions to Euler's Equations for ideal fiuid. Phys. Rev. E 51 (1995) 2059-2068. | MR

[7] F. Beltrami, Considerazioni idrodinamiche. Rend. Reale Ist. Lombardo 22 (1889) 121-130. | JFM

[8] M. A. Berger and G. B. Field, The topological properties of magnetic helicity. J. Fluid Mech. 147 (1984) 133-148. | MR

[9] O. Bjorgum, On Beltrami vector fields and flows, Part I, Univ. Bergen Årbok, Naturv. rekke. No. 1 (1951). | MR

[10] O. Bjorgum, On Beltrami vector fields and flows, Part II, Univ. Bergen Årbok, Naturv. rekke. No. 13 (1952). | MR

[11] T. Z. Boulmezaoud, On the linear force-free fields in a bounded domain and in a half-cylinder of R3. C. R. Acad. Sci. 325 (1997) 1235-1240. | MR | Zbl

[12] T. Z. Boulmezaoud, Y. Maday and T. Amari, On the existence of non-linear force-free fields in a bounded domain. SIAM J. Appl. Math. (submitted).

[13] T. Z. Boulmezaoud, Étude des champs de Beltrami dans des domaines de R3 bornés et non-bornés et applications en astro-physique. Ph.D. thesis, Laboratoire d'Analyse Numérique, University of Pierre et Marie Curie, France (1998).

[14] S. Chandrasekhar and P. C. Kendal, On Force-free magnetic fields. Astrophys. J. 126 (1957) 457-460. | MR

[15] P. Constantin and A. Majda, The Beltrami Spectrum for incompressible fluid flows. Comm. Math. Phys. 115 (1988) 435-456. | MR | Zbl

[16] R. Dautray and J.-L. Lions, Analyse mathématique et calcul numérique, Tome 5. Masson, Paris (1988).

[17] P. Démoulin, E. R. Priest and U. Anzer, A three-dimensional model for solar prominences. Astron. Astrophys. 221 (1989)326-337.

[18] J.-M. Dominguez, Étude des équations de la Magnétohydrodynamique stationnaires et leur approximation par élements finis, thèse de Docteur Ingénieur. University of Pierre et Marie Curie, France (1982).

[19] D. Dritshel, Generalized helical Beltrami flows in hydrodynamics and magnetohydrodynamics. J. Fluid Mech. 222 (1991) 525-541. | MR | Zbl

[20] G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique. Dunod, Paris (1972). | MR | Zbl

[21] C. J. Durant, Linear Force-free fields and coronal models. Aust. J. Phys. 42 (1989) 317-329.

[22] C. Foias and R. Temam, Remarques sur les équations de Navier-Stockes et phénomènes successifs de bifurcation, Ann. Sc. Norm. Sup. Pisa. S. 4 5 (1978) 29-63. | Numdam | MR | Zbl

(23] K. O. Friedrichs, Differential forms on Reimannian manifolds. Comm. Pure Appl. Math. 8 (1955) 551-590. | MR | Zbl

[24] H. P. Furth, S. C. Jardin and D. B. Montgomery, Force-free Coil principles Applied to High-Temperature Superconducting Materials. IEEE Trans. Magnet. 24 (1998) 1467-1468.

[25] V. Girault and P. A. Raviart, Finite element methods for Navier-Stokes equations. Springer-Verlag (1986). | MR | Zbl

[26] J. Gobert, Sur une inégalité de coercivité. J. Math. Anal. Appl. 36 (1971) 518-528. | MR | Zbl

[27] H. Grad and H. Rubin, Hydromagnetic equilibria and force force free fields, in Proc. 2nd Intern. Conf. on Peaceful Uses of Atomic Energy, Geneva, United Nations 31 (1958) 190-197.

[28] N. M. Günter, Potential Theory. Ungar Ed. (1967).

[29] T. H. Jensen and M. S. Chu Current drive and helicity injection, Phys. Fluids 27 (1994) 2881-2885. | Zbl

[30] R. Kress, Ein Neumannsches Randwertproblem ber kraftfreien Feldern. Mech. Verf. Math. Phys. 7 (1972) 81-97. | MR | Zbl

[31] R. Kress, The treatment of a Neumann boundary value problem for force-free fields by an integral equation method. Proceedings of the Royal Society of Edimburgh 82 (1978) 71-86. | MR | Zbl

[32] R. Kress, A remark on a boundary value problem for force-free fields. J. Appl. Math. Phys. 28 (1977) 715-722. | MR | Zbl

[33] P. Laurence and M. Avellaneda, On Woltjer's variational principle for force-free fields. J. Math. Phys. 32 (1991) 1240-1253. | MR | Zbl

[34] F. Marqués, On boundary conditions for velocity potentials in confined flows, application to couette flow. Phys. Fluids. A 2 (1990) 729-737. | MR | Zbl

[35] G. E. Marsh, Magnetic energy, multiply connected domains and force free fields. Phys. Rev. A 46 (1992) 2117-2123. | MR

[36] G. E. Marsh, Helicity, topology and Force-free fields. Phys. Rev. E. 47(1992)3607-3611. | MR

[37] H. K. Moffatt, The degree of knottedness of tangled vortes lines. J. Fluid. Mech 35 (1969) 117-129. | Zbl

[38] D. Mclaughlin and O. Pironneau, Some notes on penodic Beltrami fields in Cartesian geometry. J. Math. Phys. 32 (1991)797-804. | MR | Zbl

[39] H. E. Moses, Eigenfunctions of the curl operator, rotationally invariant Helmoltz theorem, and applications to electromagnetic theory and fluid mechanics. SIAM J. Appl. Math. 21 (1971) 114-144. | MR | Zbl

[40] C. Nedelec, Équations intégrales. Cours de D. E. A. d'Analyse Numérique, University of Pierre et Marie Curie, France (1995).

[41] R. Picard, Ein Randwertproblem in der Theorie kraftfreier Magnetfelfer. Zeit. Angew. Math. Phys. 27 (1976) 196-180. | MR | Zbl

[42] E. R. Priest, Solar Magnetohydrodynamics. Reidel, Dordrecht (1982).

[43] T. Sakurai, Computational modelmg of magnetic fields in solar active regions. Space Sci. Rev. 51 (1989) 11-48.

[44] N. Seehafer, Determination of constant α force-free fields from magnetograph data. Solar Phys. 58 (1978) 215-223.

[45] V. D. Shafranov, On magnetohydrodynamical Equilibrium configurations. Soviet. Phys. JETP 6 (1958) 545-554. | MR | Zbl

[46] J. B. Taylor, Relaxation of toroidal plasma and generation of reverse magnetic fields. Phys. Rev. Lett. 33 (1974) 1139-1141.

[47] J. B. Taylor, Relaxation of magnetic reconnection in plasmas. Rev. Mod. Phys. 58 (1986) 741-763.

[48] Z. Yoshida and Y. Giga, Remarks on spectra of operator Rot. Math. Z. 204 (1990) 235-245. | MR | Zbl

[49] C. Y. Wang, Exact solutions of the steady-state Navier-Stokes equations. Annu. Rev. Fluid Mech. 23 (1991)159-177. | Zbl

[50] L. Woltjer, Proc.Nat. Acad. Sci. 44 (1958) 489. | Zbl