e-book On the blow-up threshold for weakly coupled nonlinear Schrödinger equations

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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.

Adami , G. Golse , A. Aizenman , E. Lieb , R. Seiringer , J. Solovej , J.

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