SMALL DATA SCATTERING FOR CUBIC DIRAC EQUATION WITH HARTREE TYPE NONLINEARITY IN R1+3

摘要

We prove that the initial value problem for the Dirac equation (-i gamma(mu)partial derivative(mu) + m)psi = (e(-vertical bar x vertical bar)/vertical bar x vertical bar*((psi) over bar psi))psi in R-1(+3) is globally well-posed and the solution scatters to free waves asymptotically as t -> +/-infinity if we start with initial data that are small in H-s for s > 0. This is an almost critical well-posedness result in the sense that L-2 is the critical space for the equation. The main ingredients in the proof are Strichartz estimates, space-time bilinear null-form estimates for free waves in L-2, and an application of the U-p and V-p function spaces.