Virial identity and weak dispersion for the magnetic Dirac equation

Authors :: Nabile Boussaid
Luca Fanelli
Piero D'Ancona
Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB)
Université de Bourgogne (UB)-Université de Franche-Comté (UFC)
Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS)
Dipartimento di Matematica 'Guido Castelnuovo' [Roma I] (Sapienza University of Rome)
Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome]
Departamento de Matematicas
Universidad del Pais Vasco / Euskal Herriko Unibertsitatea [Espagne] (UPV/EHU)
Publication Year :: 2009
Publisher :: HAL CCSD, 2009.
Abstract: We analyze the dispersive properties of a Dirac system perturbed with a magnetic field. We prove a general virial identity; as applications, we obtain smoothing and endpoint Strichartz estimates which are optimal from the decay point of view. We also prove a Hardy-type inequality for the perturbed Dirac operator.<br />13 pages, typos in the statement of theorem 1.3 and clarification of the proof in subsection 3.2

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