Energy conservation and blowup of solutions for focusing Gross–Pitaevskii hierarchies
Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 5, p. 1271-1290
We consider solutions of the focusing cubic and quintic Gross–Pitaevskii (GP) hierarchies. We identify an observable corresponding to the average energy per particle, and we prove that it is a conserved quantity. We prove that all solutions to the focusing GP hierarchy at the L 2 -critical or L 2 -supercritical level blow up in finite time if the energy per particle in the initial condition is negative. Our results do not assume any factorization of the initial data.
@article{AIHPC_2010__27_5_1271_0,
     author = {Chen, Thomas and Pavlovi\'c, Nata\v sa and Tzirakis, Nikolaos},
     title = {Energy conservation and blowup of solutions for focusing Gross--Pitaevskii hierarchies},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {27},
     number = {5},
     year = {2010},
     pages = {1271-1290},
     doi = {10.1016/j.anihpc.2010.06.003},
     zbl = {1200.35253},
     mrnumber = {2683760},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2010__27_5_1271_0}
}
Chen, Thomas; Pavlović, Nataša; Tzirakis, Nikolaos. Energy conservation and blowup of solutions for focusing Gross–Pitaevskii hierarchies. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 5, pp. 1271-1290. doi : 10.1016/j.anihpc.2010.06.003. http://www.numdam.org/item/AIHPC_2010__27_5_1271_0/

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