On the Klainerman–Machedon conjecture for the quantum BBGKY hierarchy with self-interaction
We consider the 3D quantum BBGKY hierarchy which corresponds to the -particle Schrödinger equation. We assume the pair interaction is . For the interaction parameter , we prove that, provided an energy bound holds for solutions to the BBKGY hierarchy, the limit points satisfy the space-time bound conjectured by S. Klainerman and M. Machedon [45] in 2008. The energy bound was proven to hold for in [28]. This allows, in the case , for the application of the Klainerman–Machedon uniqueness theorem...