Mass-Energy threshold dynamics for dipolar Quantum Gases

We 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.


Year:
Sep 14 2020
Other identifiers:
Laboratories:


Note: The status of this file is: Anyone


 Record created 2020-09-14, last modified 2020-10-29

Fulltext:
Download fulltext
PDF

Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)