Sharp threshold of global well-posedness vs finite time blow-up for a class of inhomogeneous Choquard equations

Abstract

It is the purpose of this work to obtain a sharp threshold of global existence vs blow-up dichotomy for mass-super-critical and energy subcritical solutions to an inhomogeneous Choquard equation.

Scattering for the non-radial focusing inhomogeneous nonlinear Schrödinger-Choquard equation

“…In particular, if u is uniformly bounded in H 1 , then it is global. For more details, we refer the reader to [1,13].…”

“…We briefly review some of the variational analysis related to the ground state Q. For more details, see [1,13].…”

“…For the Eq. (1.1), Alharbi-Saanouni [1] studied the local theory and finite time blow-up. In [14], Saanouni proved the scattering theory with the radial setting.…”

“…We refer to Alharbi-Saanouni [1] about the existence of the ground state for the above elliptic equation. The uniqueness is still open.…”

Scattering theory for a class of radial focusing inhomogeneous Hartree equations

“…To the author knowledge, the inhomogeneous Choquard problem, was only treated in [1], where the local well-posedness in the energy space was proved via an adapted Gagliardo-Nirenberg type identity. In the focusing regime, a threshold of global existence versus finite time blow-up of solutions was obtained.…”