| Abstract: |
| We consider a generalization of the focusing Hartree equation, a nonlinear Schrodinger-type equation with convolution nonlinearity, and discuss basic properties of solutions in the intercritical regime. In particular, similar to the standard nonlinear Schrodinger equation, we address the well-posedness questions, dichotomy for globally existing in time and scattering solutions vs finite time blow-up. To obtain scattering we employ methods of concentration compactness of Kenig-Merle and a recently developed one by Dodson-Murphy. |
|