Well-posedness in weighted spaces for the generalized Hartree equation with $p<2$

Anudeep K. Arora, Oscar Riaño, Svetlana Roudenko

We investigate the well-posedness in the generalized Hartree equation $i{u}_t+\Delta u+(|x{|}^{-(N-\gamma )}\ast |u{|}^p)|u{|}^{p-2}u=0$, $x\in {\mathbb{R}}^N$, $0<\gamma <N$, for low powers of nonlinea…