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We prove that the initial value problem for Force-free Electrodynamics in Euler variables is not well posed.
Jean Leray. Hyperbolic differential equations, mimeographed notes. Institute for Advanced Study, Princeton, 1953
1953
Earlier work this paper cites.
Kurt Otto Friedrichs. Symmetric hyperbolic linear differential equations. Comm. Pure Appl. Math. 7 (1954), 345-392. 1954
1954
Earlier work this paper cites.
Gilbert Strang. Necessary and insufficient conditions for well-posed Cachy problems. J.Differential equations, 2 p.107-114, 1966
1966
Earlier work this paper cites.
Jean Leray and Yujiro Ohya. Équations et systèmes non-linéaires, hyperboliques nonstricts. Math. Ann. 170, pp. 167–205, 1967
1967
Earlier work this paper cites.
David Stern. Euler Potentials. American Journal of Physics 38, 494 (1970); doi: 10.1119/1.1976373, 1970
1970
Earlier work this paper cites.
Heinz-Otto Kreiss. Initial boundary value problems for hyperbolic systems. Commun. Pur. Appl. Math., 23:277–298, 1970
1970
Earlier work this paper cites.
Brandon Carter, in General Relativity: An Einstein Centenary Survey, edited by S. W. Hawking and W. Israel Cambridge University Press, Cambridge, England, 1979
1979
Earlier work this paper cites.
Kip S. Thorne and Douglas Macdonald. Electrodynamics in curved spacetime: 3+ 1 formulation. Monthly Notices of the Royal Astronomical Society, 198(2):339–343, 1982
1982
Earlier work this paper cites.
Yvonne Choquet-Bruhat, Cecile Dewitt-Morette and Margaret Dillard-Bleick. Analysis, manifolds and physics. Vol. 1, Revised Edition, Elsevier, 1982
1982
Earlier work this paper cites.
Joel Smoller. Shock Waves and Reaction—Diffusion Equations. Grundlehren der mathematischen Wissenschaften 258 series, 2nd. edition, Springer US. 1983
1983
Earlier work this paper cites.
Roger Penrose and Wolfgang Rindler. Spinors and Spacetime, Volume 1: two spinors calculus and relativistic fields. Cambridge University Press. ISBN 0 521 24527 3, 1984
1984
Cited alongside, same era.
Robert Wald. General Relativity. University of Chicago Press. ISBN-10: 0226870332, 1984
1984
Cited alongside, same era.
Heinz-Otto Kreiss and Jens Lorenz. Initial Boundary Value Problems and the Navier-Stokes Equations. Academic Press, San Diego, USA, ISBN 0-12-426125-6, 1989
1989
Cited alongside, same era.
Michael E. Taylor. Pseudodifferential operators and nonlinear PDE. Progress in Mathematics 100, Birkhäuser, Boston, USA, 1991
1991
Cited alongside, same era.
Robert P. Geroch. Partial differential equations of physics. [Online Los Alamos Archive Preprint]: cited on 19 January 1998, http: //xxx.lanl.gov/abs/gr-qc/9602055. Scottish Summer School in Theo- retical Physics. 1996
S. S. Komissarov. Time-dependent, force-free, degenerate electrodynamics. Monthly Notices of the Royal Astronomical Society, 336(3):759–766, 2002
2002
Later among the works it cites.
Oscar Reula. Strongly hyperbolic systems in General Relativity. Journal of Hyperbolic Equations, Vol. 1, No. 2 (2004) p. 251-269. 2004
2004
Later among the works it cites.
Sorin Zaharia. Improved Euler potential method for three-dimensional magnetospheric equilibrium. Journal of Geophysical Research, Vol. 113, A08221, doi:10.1029/2008JA013325, 2008
2008
Later among the works it cites.
Yvonne Choquet-Bruhat. General Relativity and the Einstein Equations. Oxford Mathematical Monographs, 0199230722, 2008
2008
Later among the works it cites.
Axel Brandenburg. Magnetic field evolution in simulations with Euler potentials. Mon. Not. R. Astron. Soc. 401, 347–354. doi:10.1111/j.1365-2966.2009.15640.x, 2010
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1996
Cited alongside, same era.
Toshio Uchida. Theory of force-free electromagnetic fields. I. General Theory. Phys. Rev. E, 56:2181–2197, 1997
1997
Cited alongside, same era.
Toshio Uchida. Theory of force-free electromagnetic fields. II. Configuration with symmetry. Phys. Rev. E 56, 2198, 1997
1997
Cited alongside, same era.
Oscar Reula. Hyperbolic Methods for Einstein’s Equations. Living Reviews in Relativity Electronic Publication www.livingreviews.org/Articles/Volume1/1998-3reula/, 1998
1998
Cited alongside, same era.
Keinz-Otto Kreiss and Omar E. Ortiz. Some Mathematical And Numerical Questions Connected With First And Second Order Time Dependent Systems Of Partial Differential Equations. arXiv:gr-qc/0106085. Lect.Notes Phys. 604 (2002) 359. 2001
2001
Cited alongside, same era.
2010
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2013
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Samuel E Gralla and Ted Jacobson. Spacetime approach to force-free magnetospheres. Monthly Notices of the Royal Astronomical Society, 445(3):2500–2534, 2014
2014
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Fernando Abalos, Federico Carrasco, Erico Goulart, and Oscar Reula. Nonlinear electrodynamics as a symmetric hyperbolic system. Phys. Rev. D, 92:084024, 2015
2015
Later among the works it cites.
Federico Carrasco and Oscar Reula. Covariant Hyperbolization of Force-free Electrodynamics. Phys. Rev. D, 93.93.085013, 2016
2016
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