Dinh, Van DuongForcella, LuigiHajaiej, Hichem2020-09-142020-09-142020-09-14202210.4310/CMS.2022.v20.n1.a5https://infoscience.epfl.ch/handle/20.500.14299/171668WOS:0007315841000052009.05933v1We consider a Gross-Pitaevskii equation which appears as a model in the description of dipolar Bose-Einstein condensates, without a confining external trapping potential. We describe the asymptotic dynamics of solutions to the corresponding Cauchy problem in the energy space in different configurations with respect to the mass-energy threshold, namely for initial data above and at the mass-energy threshold. We first establish a scattering criterion for the equation that we prove by means of the concentration/compactness and rigidity scheme. This criterion enables us to show the energy scattering for solutions with data above the mass-energy threshold, for which only blow-up was known. We also prove a blow-up/grow-up criterion for the equation with general data in the energy space. As a byproduct of scattering and blow-up criteria, and the compactness of minimizing sequences for the Gagliardo-Nirenberg's inequality, we study long time dynamics of solutions with data lying exactly at the mass-energy threshold.gross-pitaevskii equationdipolar becenergy scatteringfinite-time blow-upconcentration phenomenagross-pitaevskii equationbose-einstein condensationblow-upscatteringtext::journal::journal article::research article