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

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.

MSC:

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