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arXiv · 1011.4641

Local well-posedness for Gross-Pitaevskii hierarchies

Zeqian Chen
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Abstract

We consider the Cauchy problem for the Gross-Pitaevskii infinite linear hierarchy of equations on $\mathbb{R}^n.$ By introducing a (F)-norm in certain Sobolev type spaces of sequences of marginal density matrices, we establish local existence, uniqueness and stability of solutions. Explicit space-time type estimates for the solutions are obtained as well. In particular, this (F)-norm is compatible with the usual Sobolev space norm whenever the initial data is factorized.

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Zeqian Chen. 2014-03-11. Local well-posedness for Gross-Pitaevskii hierarchies. https://arxiv.org/abs/1011.4641

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