Asymptotic estimates for the wave functions of the Dirac-Coulomb operator and applications

Federico Cacciafesta (1) , Éric Séré (2) , Junyong Zhang (3)

1 Dipartimento di Matematica [Padova]
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 Department of Mathematics, Beijing Institute of Technology

In this paper we prove some uniform asymptotic estimates for confluent hypergeometric functions making use of the steepest-descent method. As an application, we obtain Strichartz estimates that are L2-averaged over angular direction for the massless Dirac-Coulomb equation in 3D.

Keywords: Dirac-Coulomb equation; Strichartz estimates; steepest descent method

Domains: Analysis of PDEs [math.AP]; Mathematical Physics [math-ph]

Federico Cacciafesta, Éric Séré, Junyong Zhang. Asymptotic estimates for the wave functions of the Dirac-Coulomb operator and applications. Communications in Partial Differential Equations, 2023, 48 (3), pp.355-385. ⟨10.1080/03605302.2023.2169938⟩. ⟨hal-04045473⟩