Wednesday, May 8, 2013

1305.1404 (Kenneth Taliaferro et al.)

Positive Semidefiniteness and Global Well-Posedness of Solutions to the
Gross-Pitaevskii Hierarchy

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 $N\rightarrow\infty$.
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