@article{M2AN_1999__33_2_359_0, author = {Boulmezaoud, Tahar-Zam\`ene and Maday, Yvon and Amari, Tahar}, title = {On the linear force-free fields in bounded and unbounded three-dimensional domains}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {359--393}, publisher = {EDP-Sciences}, volume = {33}, number = {2}, year = {1999}, mrnumber = {1700040}, zbl = {0954.35043}, language = {en}, url = {http://archive.numdam.org/item/M2AN_1999__33_2_359_0/} }
TY - JOUR AU - Boulmezaoud, Tahar-Zamène AU - Maday, Yvon AU - Amari, Tahar TI - On the linear force-free fields in bounded and unbounded three-dimensional domains JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1999 SP - 359 EP - 393 VL - 33 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/item/M2AN_1999__33_2_359_0/ LA - en ID - M2AN_1999__33_2_359_0 ER -
%0 Journal Article %A Boulmezaoud, Tahar-Zamène %A Maday, Yvon %A Amari, Tahar %T On the linear force-free fields in bounded and unbounded three-dimensional domains %J ESAIM: Modélisation mathématique et analyse numérique %D 1999 %P 359-393 %V 33 %N 2 %I EDP-Sciences %U http://archive.numdam.org/item/M2AN_1999__33_2_359_0/ %G en %F M2AN_1999__33_2_359_0
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://archive.numdam.org/item/M2AN_1999__33_2_359_0/
[1] On the eigenfuntions and on the eigenvalnes of general elliptic boundary value problems. Comm. Pure Appl. Math.15 (1962) 119-147. | MR | Zbl
,[2] On the computation of constant α force-free fields. Astron. Astrophys. 100 (1981) 197-200.
,[3] 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] On some properties of force-free magnetic fields in infinite regions of space. Astrophys. J. 283 (1984) 349-362.
,[5] Reconstructing the solar coronal magnetic field as a force free magnetic field. Solar Physics 174 (1997) 129-149.
, , , and ,[6] Complex Trkalian fields and solutions to Euler's Equations for ideal fiuid. Phys. Rev. E 51 (1995) 2059-2068. | MR
and ,[7] Considerazioni idrodinamiche. Rend. Reale Ist. Lombardo 22 (1889) 121-130. | JFM
,[8] The topological properties of magnetic helicity. J. Fluid Mech. 147 (1984) 133-148. | MR
and ,[9] On Beltrami vector fields and flows, Part I, Univ. Bergen Årbok, Naturv. rekke. No. 1 (1951). | MR
,[10] On Beltrami vector fields and flows, Part II, Univ. Bergen Årbok, Naturv. rekke. No. 13 (1952). | MR
,[11] 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] On the existence of non-linear force-free fields in a bounded domain. SIAM J. Appl. Math. (submitted).
, and ,[13] 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] On Force-free magnetic fields. Astrophys. J. 126 (1957) 457-460. | MR
and ,[15] The Beltrami Spectrum for incompressible fluid flows. Comm. Math. Phys. 115 (1988) 435-456. | MR | Zbl
and ,[16] Analyse mathématique et calcul numérique, Tome 5. Masson, Paris (1988).
and ,[17] A three-dimensional model for solar prominences. Astron. Astrophys. 221 (1989)326-337.
, and ,[18] 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] Generalized helical Beltrami flows in hydrodynamics and magnetohydrodynamics. J. Fluid Mech. 222 (1991) 525-541. | MR | Zbl
,[20] Les inéquations en mécanique et en physique. Dunod, Paris (1972). | MR | Zbl
and ,[21] Linear Force-free fields and coronal models. Aust. J. Phys. 42 (1989) 317-329.
,[22] 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
and ,(23] Differential forms on Reimannian manifolds. Comm. Pure Appl. Math. 8 (1955) 551-590. | MR | Zbl
,[24] Force-free Coil principles Applied to High-Temperature Superconducting Materials. IEEE Trans. Magnet. 24 (1998) 1467-1468.
, and ,[25] Finite element methods for Navier-Stokes equations. Springer-Verlag (1986). | MR | Zbl
and ,[26] Sur une inégalité de coercivité. J. Math. Anal. Appl. 36 (1971) 518-528. | MR | Zbl
,[27] 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.
and ,[28] Potential Theory. Ungar Ed. (1967).
,[29] Current drive and helicity injection, Phys. Fluids 27 (1994) 2881-2885. | Zbl
and[30] Ein Neumannsches Randwertproblem ber kraftfreien Feldern. Mech. Verf. Math. Phys. 7 (1972) 81-97. | MR | Zbl
,[31] 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] A remark on a boundary value problem for force-free fields. J. Appl. Math. Phys. 28 (1977) 715-722. | MR | Zbl
,[33] On Woltjer's variational principle for force-free fields. J. Math. Phys. 32 (1991) 1240-1253. | MR | Zbl
and ,[34] On boundary conditions for velocity potentials in confined flows, application to couette flow. Phys. Fluids. A 2 (1990) 729-737. | MR | Zbl
,[35] Magnetic energy, multiply connected domains and force free fields. Phys. Rev. A 46 (1992) 2117-2123. | MR
,[36] Helicity, topology and Force-free fields. Phys. Rev. E. 47(1992)3607-3611. | MR
,[37] The degree of knottedness of tangled vortes lines. J. Fluid. Mech 35 (1969) 117-129. | Zbl
,[38] Some notes on penodic Beltrami fields in Cartesian geometry. J. Math. Phys. 32 (1991)797-804. | MR | Zbl
and ,[39] 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] Équations intégrales. Cours de D. E. A. d'Analyse Numérique, University of Pierre et Marie Curie, France (1995).
,[41] Ein Randwertproblem in der Theorie kraftfreier Magnetfelfer. Zeit. Angew. Math. Phys. 27 (1976) 196-180. | MR | Zbl
,[42] Solar Magnetohydrodynamics. Reidel, Dordrecht (1982).
,[43] Computational modelmg of magnetic fields in solar active regions. Space Sci. Rev. 51 (1989) 11-48.
,[44] Determination of constant α force-free fields from magnetograph data. Solar Phys. 58 (1978) 215-223.
,[45] On magnetohydrodynamical Equilibrium configurations. Soviet. Phys. JETP 6 (1958) 545-554. | MR | Zbl
,[46] Relaxation of toroidal plasma and generation of reverse magnetic fields. Phys. Rev. Lett. 33 (1974) 1139-1141.
,[47] Relaxation of magnetic reconnection in plasmas. Rev. Mod. Phys. 58 (1986) 741-763.
,[48] Remarks on spectra of operator Rot. Math. Z. 204 (1990) 235-245. | MR | Zbl
and ,[49] Exact solutions of the steady-state Navier-Stokes equations. Annu. Rev. Fluid Mech. 23 (1991)159-177. | Zbl
,[50] Zbl
, Proc.Nat. Acad. Sci. 44 (1958) 489. |