On the Cauchy problem for Gross-Pitaevskii hierarchies

The purpose of this paper is to investigate the Cauchy problem for the Gross-Pitaevskii infinite linear hierarchy of equations on $\mathbb{R}^n,$ $n \geq 1.$ We prove local existence and uniqueness of solutions in certain Sobolev type spaces $\mathrm{H}^α_ξ$ of sequences of marginal density operators with $α> n/2.$ In particular, we give a clear discussion of all cases $α> n/2,$ which covers the local well-posedness problem for Gross-Pitaevskii hierarchy in this situation.

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