Local well-posedness below the charge norm for the Dirac-Klein-Gordon system in two space dimensions

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dc.creatorD'Ancona, Piero
dc.creatorFoschi, Damiano
dc.creatorSelberg, Sigmund
dc.date2006-06-23
dc.date.accessioned2026-07-07T07:17:36Z
dc.date.available2026-07-07T07:17:36Z
dc.descriptionWe prove that the Cauchy problem for the Dirac-Klein-Gordon equations in two space dimensions is locally well-posed in a range of Sobolev spaces of negative index for the Dirac spinor, and an associated range of spaces of positive index for the meson field. In particular, we can go below the charge norm, that is, the $L^2$ norm of the spinor. We hope that this can have implications for the global existence problem, since the charge is conserved. Our result relies on the null structure of the system, and bilinear space-time estimates for the homogeneous wave equation.
dc.description26 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/math/0606587
dc.identifierhttp://arxiv.org/abs/math/0606587
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114001
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.subject35Q40; 35L70
dc.titleLocal well-posedness below the charge norm for the Dirac-Klein-Gordon system in two space dimensions
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