In this paper we study the small-data scattering of the d dimensional fractional Schrödinger equations with d = 2, 3, Lévy index 1 < α < 2 and Hartree type nonlinearity F (u) = µ(|x|−γ ∗ |u|2)u with max (Formula presented) < γ ≤ 2, γ < d. This equation is scaling-critical in Ḣsc, (Formula presented). We show that the solution scatters in Hs,1 for any s > sc, where Hs,1 is a space of Sobolev type taking in angular regularity with norm defined by (Formula presented). For this purpose we use the recently developed Strichartz estimate which is L2 -averaged on the unit sphere Sd−1 and utilize Up -Vp space argument.
- Angularly averaged Strichartz estimate
- Hartree type fractional Schrödinger equation
- Small data scattering
- U and V spaces
ASJC Scopus subject areas