On radial solutions of semi-relativistic Hartree equations

We consider the semi-relativistic Hartree type equation with nonlocal nonlinearity $F(u) = \lambda (|x|^{-\gamma} * |u|^2)u, 0 < \gamma < n, n \ge 1$. In \cite{chooz2}, the global well-posedness (GWP) was shown for the value of $\gamma \in (0, \frac{2n}{n+1}), n \ge 2$ with large data and $\gamma \in (2, n), n \ge 3$ with small data. In this paper, we extend the previous GWP result to the case for $\gamma \in (1, \frac{2n-1}n), n \ge 2$ with radially symmetric large data. Solutions in a weighted Sobolev space are also studied.