Dispersive estimates for two-particles Schrödinger and wave equations in the Aharonov-Bohm field

Abstract: We study the dispersive behaviors of two-particles Schr\"odinger and wave equations in the Aharonov-Bohm field. In particular, we prove the Strichartz estimates for Schr\"odinger and wave equations in this setting. The key point is to construct spectral measure of Schr\"odinger operator with an Aharonov-Bohm type potential in $\R^4$. As applications, we finally prove a scattering theory for the nonlinear defocusing subcritical two-particles Schr\"odinger equation with Aharonov-Bohm potential.