dc.contributor.author | Selberg, Sigmund | |
dc.contributor.author | Tesfahun, Achenef | |
dc.date.accessioned | 2022-03-18T08:56:42Z | |
dc.date.available | 2022-03-18T08:56:42Z | |
dc.date.created | 2022-01-27T14:21:48Z | |
dc.date.issued | 2021 | |
dc.identifier.issn | 1021-9722 | |
dc.identifier.uri | https://hdl.handle.net/11250/2986064 | |
dc.description.abstract | The Maxwell–Dirac system describes the interaction of an electron with its self-induced electromagnetic field. In space dimension d=3 the system is charge-critical, that is, L2-critical for the spinor with respect to scaling, and local well-posedness is known almost down to the critical regularity. In the charge-subcritical dimensions d=1,2, global well-posedness is known in the charge class. Here we prove that these results are sharp (or almost sharp, if d=3), by demonstrating ill-posedness below the charge regularity. In fact, for d≤3 we exhibit a spinor datum belonging to Hs(Rd) for s<0, and to Lp(Rd) for 1≤p<2, but not to L2(Rd), which does not admit any local solution that can be approximated by smooth solutions in a reasonable sense. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Springer | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | Ill-posedness of the Maxwell–Dirac system below charge in space dimension three and lower | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | publishedVersion | en_US |
dc.rights.holder | Copyright 2021 The Author(s) | en_US |
dc.source.articlenumber | 42 | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 1 | |
dc.identifier.doi | 10.1007/s00030-021-00703-w | |
dc.identifier.cristin | 1991447 | |
dc.source.journal | NoDEA. Nonlinear differential equations and applications (Printed ed.) | en_US |
dc.identifier.citation | Nonlinear Differential Equations and Applications NoDEA. 2021, 28, 42. | en_US |
dc.source.volume | 28 | en_US |