Dynamics of the nonlinear Hartree equation with a focusing and defocusing perturbation. (September 2022) - Tian, Shuai; Zhu, Shihui
Abstract: In this paper, we identify the sharp energy threshold for the global existence and blow-up to the Hartree equation with a focusing and defocusing perturbation, respectively, by utilizing comprehensive potential-well structures generated by the combined nonlinearities. Then, by adopting the refined compactness lemma, we detect the dynamical properties of blow-up solutions near the sharp threshold mass, including blow-up rate, concentration, weak limits and limiting profile decomposition of blow-up solutions with small super critical mass.