Energy conservation and blowup of solutions for focusing Gross-Pitaevskii hierarchies

Details Energy conservation and blowup of solutions for focusing Gross-Pitaevskii hierarchies Energy conservation and blowup of solutions for focusing Gross-Pitaevskii hierarchies

2009-05-16

arxiv.org/abs/0905.2704v1

Ann. Inst. H. Poincare (C) Anal. Non-Lin., 27 (5), 1271-1290, 2010

Physics

Mathematical Physics

AMS Latex, 24 pages

Scientific paper

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.

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