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math.AP2008★ 4 cited
Tensor products and Correlation Estimates with applications to Nonlinear Schrödinger equations
Jim Colliander, Manoussos Grillakis, Nikolaos Tzirakis
We prove new interaction Morawetz type (correlation) estimates in one and two dimensions. In dimension two the estimate corresponds to the nonlinear diagonal analogue of Bourgain's…
math.AP2008★ 3 cited
Apriori Estimates for Many-Body Hamiltonian Evolution of Interacting Boson System
Manoussos G. Grillakis, Dionisios Margetis
We study the evolution of a many-particle system whose wave function obeys the N-body Schroedinger equation under Bose symmetry. The system Hamiltonian describes pairwise particle…