Small data scattering of semirelativistic Hartree equation

In this paper we study the small data scattering of Hartree type semirelativistic equation in space dimension 3. The Hartree type nonlinearity is [V∗|u|2]u and the potential V which generalizes the Yukawa has some growth condition. We show that the solution scatters to linear solution if an initial data given in Hs,1 is sufficiently small and s>14. Here, Hs,1 is Sobolev type space taking in angular regularity with norm defined by ‖φ‖Hs,1=‖φ‖Hs+‖∇Sφ‖Hs. To establish the results we employ the recently developed Strichartz estimate which is Lθ2-averaged on the unit sphere S2 and construct the resolution space based on Up-Vp space.