We prove endpoint estimates with angular regularity for the wave and Dirac equations perturbed with a small potential. The estimates are applied to prove global existence for the cubic Dirac equation perturbed with a small potential, for small initial H-1 data with additional angular regularity. This implies in particular global existence in the critical energy space H-1 for small radial data. (c) 2012 Elsevier Inc. All rights reserved.
Endpoint estimates and global existence for the nonlinear Dirac equation with potential / D'Ancona, Piero Antonio; Cacciafesta, Federico. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 254:5(2013), pp. 2233-2260. [10.1016/j.jde.2012.12.002]
Endpoint estimates and global existence for the nonlinear Dirac equation with potential
D'ANCONA, Piero Antonio;CACCIAFESTA, FEDERICO
2013
Abstract
We prove endpoint estimates with angular regularity for the wave and Dirac equations perturbed with a small potential. The estimates are applied to prove global existence for the cubic Dirac equation perturbed with a small potential, for small initial H-1 data with additional angular regularity. This implies in particular global existence in the critical energy space H-1 for small radial data. (c) 2012 Elsevier Inc. All rights reserved.| File | Dimensione | Formato | |
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