## Positive Semidefiniteness and Global Well-Posedness of Solutions to the Gross-Pitaevskii Hierarchy    [PDF]

Kenneth Taliaferro, Thomas Chen
We study the cubic defocusing Gross-Pitaevskii (GP) hierarchy in $\R^3$, and prove global well-posedness of solutions. In particular, we prove that positive semidefiniteness is preserved over time; so far, this property has been known for special cases, including solutions obtained from the BBGKY hierarchy of an $N$-body Schr\"odinger system as $N\rightarrow\infty$. Our approach uses a generalization of the latter in an auxiliary step, and removes a condition on the regularity of initial data used in \cite{CPBBGKY} to derive the GP hierarchy from a BBGKY hierarchy as $N\rightarrow\infty$.
View original: http://arxiv.org/abs/1305.1404