On the Cauchy problem for Gross-Pitaevskii hierarchies
Zeqian Chen, Chuangye Liu

TL;DR
This paper establishes local existence and uniqueness of solutions for the Gross-Pitaevskii hierarchy on spaces, clarifying the well-posedness in Sobolev-type spaces for /2.
Contribution
It proves local well-posedness of the Gross-Pitaevskii hierarchy in Sobolev spaces with > n/2, providing a comprehensive analysis of all such cases.
Findings
Proved local existence of solutions in > n/2 spaces.
Established uniqueness of solutions in these Sobolev spaces.
Clarified the conditions for well-posedness of the hierarchy.
Abstract
The purpose of this paper is to investigate the Cauchy problem for the Gross-Pitaevskii infinite linear hierarchy of equations on We prove local existence and uniqueness of solutions in certain Sobolev type spaces of sequences of marginal density operators with In particular, we give a clear discussion of all cases which covers the local well-posedness problem for Gross-Pitaevskii hierarchy in this situation.
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