On the Cauchy problem for Gross-Pitaevskii hierarchies

Details On the Cauchy problem for Gross-Pitaevskii hierarchies On the Cauchy problem for Gross-Pitaevskii hierarchies

2010-10-19

arxiv.org/abs/1010.3827v2

J.Math.Phys. 52, 032103(2011)

Physics

Mathematical Physics

17 pages. The referee's comments and suggestions have been incorporated into this version of the paper

Scientific paper

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 $\mathrm{H}^{\alpha}_{\xi}$ of sequences of marginal density operators with $\alpha > n/2.$ In particular, we give a clear discussion of all cases $\alpha > n/2,$ which covers the local well-posedness problem for Gross-Pitaevskii hierarchy in this situation.

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