On inhomogeneous Strichartz estimates for fractional Schrödinger equations and their applications

Abstract

In this paper we obtain some new inhomogeneous Strichartz estimates for the fractional Schrödinger equation in the radial case. Then we apply them to the well-posedness theory for the equation $i{\partial }_{t}u+|\nabla {|}^{\alpha }u=V(x,t)u$, $1<\alpha <2$, with radial ${\dot{H}}^{\gamma }$ initial data below $L^2$ and radial potentials $V\in L_t^r{L}_x^w$ under the scaling-critical range $\alpha /r+n/w=\alpha$.

To appear in Discrete Contin. Dyn. Syst., 22 pages, 2 figures