Strichartz and smoothing estimates for dispersive equations with magnetic potentials. (English) Zbl 1160.35363

D’Ancona, Piero; Fanelli, Luca

Commun. Partial Differ. Equations 33, No. 6, 1082-1112 (2008).

The authors prove global smoothing and Strichartz estimates for Schrödinger, wave, Klein-Gordon equations and for for the massless and massive Dirac systems, perturbed with electromagnetic potentials. However, the authors impose a smallness condition on the magnetic part, while the electric part can be large, while the decay and regularity conditions on the coefficients are close to critical. In particular the authors used Kato theory to prove the resolvent estimates.

Reviewer: Qutaibeh Katatbeh (Irbid)

MSC:

35B65	Smoothness and regularity of solutions to PDEs
35L05	Wave equation
58J45	Hyperbolic equations on manifolds

Keywords:

hyperbolic equations; Schödinger equation; small magnetic part; Klein-Gordon equations