Strichartz estimates for magnetic Schrödinger, wave and Klein-Gordon equations in exterior domain and application to scattering theory (Q6046556)

The authors of this paper derive Strichartz estimates for solutions of magnetic Schrödinger equations, wave equations, and Klein-Gordon equations in domains with non-trivial topology (e.g. in exterior to the star-shaped obstacle). Their proof is based on smoothing estimates for solutions of the perturbed equations and the Strichartz estimates for solutions of the free equations. The authors use their results to prove scattering for these equations in the case of power type nonlinearity.