TY - JOUR
T1 - Dynamical collapse of cylindrical symmetric dipolar Bose–Einstein condensates
AU - Bellazzini, Jacopo
AU - Forcella, Luigi
N1 - Funding Information:
J. B. is partially supported by Project 2016 “Dinamica di equazioni nonlineari dispersive” from FONDAZIONE DI SARDEGNA. L.F. was supported by the EPSRC New Investigator Award (grant no. EP/S033157/1).
Publisher Copyright:
© 2021, The Author(s).
PY - 2021/12
Y1 - 2021/12
N2 - We study the formation of singularities for cylindrical symmetric solutions to the Gross–Pitaevskii equation describing a dipolar Bose–Einstein condensate. We prove that solutions arising from initial data with energy below the energy of the Ground State and that do not scatter collapse in finite time. The main tools to prove our result are the variational characterization of the Ground State energy, suitable localized virial identities for cylindrical symmetric functions, and general integral and pointwise estimates for operators involving powers of the Riesz transform.
AB - We study the formation of singularities for cylindrical symmetric solutions to the Gross–Pitaevskii equation describing a dipolar Bose–Einstein condensate. We prove that solutions arising from initial data with energy below the energy of the Ground State and that do not scatter collapse in finite time. The main tools to prove our result are the variational characterization of the Ground State energy, suitable localized virial identities for cylindrical symmetric functions, and general integral and pointwise estimates for operators involving powers of the Riesz transform.
UR - http://www.scopus.com/inward/record.url?scp=85115154786&partnerID=8YFLogxK
U2 - 10.1007/s00526-021-02096-1
DO - 10.1007/s00526-021-02096-1
M3 - Article
AN - SCOPUS:85115154786
VL - 60
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
SN - 0944-2669
IS - 6
M1 - 229
ER -