The local well-posedness for Gross-Pitaevskii hierarchies

Details The local well-posedness for Gross-Pitaevskii hierarchies The local well-posedness for Gross-Pitaevskii hierarchies

2010-11-21

arxiv.org/abs/1011.4641v2

Physics

Mathematical Physics

19 pages. Minor correction

Scientific paper

We consider the Cauchy problem for the Gross-Pitaevskii infinite linear hierarchy of equations on $\mathbb{R}^n.$ By introducing a quasi-norm in certain Sobolev type spaces of sequences of marginal density matrices, we establish local existence, uniqueness and stability of solutions. This quasi-norm is compatible with the usual Sobolev space norm when the initial data is factorized. Explicit space-time type estimates for the solutions are obtained. The results hold without the assumption of factorized initial conditions.

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