Local well-posedness for Gross-Pitaevskii hierarchies

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.

16 pages. Published version

References in corpus (2)

• Rigorous Derivation of the Gross-Pitaevskii Equation
• Energy conservation and blowup of solutions for focusing Gross-Pitaevskii hierarchies

Cited by in corpus (1)

• Blowup alternative for Gross-Pitaevskii hierarchies