Multilinear Morawetz identities for the Gross-Pitaevskii hierarchy

Abstract

This article consists of two parts. In the first part, we review the most recent proofs establishing quadratic Morawetz inequalities for the nonlinear Schrödinger equation (NLS). We also describe the applications of these estimates to the problem of quantum scattering. In the second part, we generalize some of the methods developed for the NLS by many authors to the case of Gross-Pitaevskii (GP) hierarchies. In particular, we prove both regular and interaction Morawetz identities for the GP hierarchy, which appear here for the first time in the literature.

25 pages, AMS Latex

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• Focusing Quantum Many-body Dynamics: The Rigorous Derivation of the 1D Focusing Cubic Nonlinear Schrödinger Equation
• On the Rigorous Derivation of the 3D Cubic Nonlinear Schrödinger Equation with A Quadratic Trap
• On the uniqueness of solutions to the periodic 3D Gross-Pitaevskii hierarchy
• Randomization and the Gross-Pitaevskii hierarchy
• On the well-posedness and scattering for the Gross-Pitaevskii hierarchy via quantum de Finetti