In this paper we study the small-data scattering of Hartree type fractional Schrödinger equations in space dimension 2, 3. It has Lévy index a between 1 and 2, and Hartree type nonlinearity F(u) = µ(|x|-y*|u|2)u with 2d/(2d - 1) < y < 2, y ≥ α > 1. This equation is scaling-critical in Hsc with sc (y-α)/2. We show that the solution scatters in Hsc,1 where Hsc, 1 is also a scaling critical space of Sobolev type taking in angular regularity with norm defined by. For this purpose we use the recently developed Strichartz estimate which is L2θ -averaged on the unit sphere Sd-1.
- Angularly averaged strichartz estimate
- Hartree type fractional schrödinger equation
- Scaling critical space
- Small data scattering
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology