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We prove endpoint estimates with angular regularity for the wave and Diracequations perturbed with a small potential. The estimates are applied to proveglobal existence for the cubic Dirac equation perturbed with a small potential,for small initial $H^{1}$ data with additional angular regularity. This impliesin particular global existence in the critical energy space $H^{1}$ for smallradial data.

Endpoint estimates and global existence for the nonlinear Dirac equation with potential