Strichartz estimates for a Schr\"odinger equation on the half-line with a Neumann boundary condition

Abstract

In this paper we prove some new Strichartz estimates related to the Cauchy problem for the Bessel operator on the half-line and we establish a fractal version of the Tomas-Stein restriction theorem for the Hankel transform. Then we use the proved Strichartz estimates to show global in time well-posedness for a class of nonlinear $L^2_a$-critical problems, and local in time well-posedness in the sub-critical case.