Derivation in strong topology and global well-posedness of solutions to the Gross-Pitaevskii hierarchy

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We derive the cubic defocusing GP hierarchy in R³ from a bosonic N-particle Schrödinger equation as N→∞, in the strong topology corresponding to the space Hξ¹ introduced in chpa. In particular, we thereby eliminate the requirement of regularity Hξ¹⁺ for the initial data used in CPBBGKY. Moreover, the marginal density matrices obtained in this strong limit are allowed to be of infinite rank. This contrasts previous results where weak-* limits were derived, and subsequently enhanced to strong limits based on the condition that the limiting density matrices have finite rank. Furthermore, we prove that positive semidefiniteness of marginal density matrices is preserved over time, which we combine with results in CPHE, to obtain the global well-posedness of solutions.