Strichartz and smoothing estimates for dispersive equations with magnetic potentials

2007/02/13 by D'Ancona, Piero, Fanelli, Luca · 3 citations
#35L05 #58J45 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.math/0702362

Abstract

We prove global smoothing and Strichartz estimates for the Schroedinger, wave, Klein-Gordon equations and for the massless and massive Dirac systems, perturbed with singular electromagnetic potentials. We impose a smallness condition on the magnetic part, while the electric part can be large. The decay and regularity assumptions on the coefficients are close to critical.

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• Decay estimates for one Aharonov-Bohm solenoid in a uniform magnetic field III: Product cones
• Generalized Strichartz estimates for the massive Dirac equation with critical potentials
• Blow up for nonlinear wave-type equations with perturbed derivatives

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