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We study the 2D-wave equation with a scaling-critical electromagneticpotential. This problem is doubly critical, because of the scaling invarianceof the model and the singularities of the potentials, which are not locallyintegrable. In particular, the diamagnetic phenomenon allows to considernegative electric potential which can be singular in the same fashion as theinverse-square potential. We prove sharp time-decay estimates in the purelymagnetic case, and Strichartz estimates for the complete model, involving acritical electromagnetic field.

Dispersive estimates for 2D-wave equations with critical potentials