152 citations · 579 across the 8 of their papers we have counts for
8 papers
Global estimates for the Hartree-Fock-Bogoliubov equations
Jacky Jia Wei Chong, Manoussos G. Grillakis, Matei Machedon +1
We prove that certain Sobolev-type norms, slightly stronger than those given by energy conservation, stay bounded uniformly in time and . This allows one to extend the local exi…
Counterexamples to collapsing estimates
Xiumin Du, Matei Machedon
We show that certain space-time estimates for generalized density matrices which have been used by several authors in recent years to study equations of BBGKY or Hartree-Fock…
Beyond mean field: On the role of pair excitations in the evolution of condensates
M. Grillakis, M. Machedon
This paper (published in 2013) introduces a refinement of the equations for the pair excitation function used in our previous work with D. Margetis. The new equations are Euler-Lag…
Pair excitations and the mean field approximation of interacting Bosons, II
M. Grillakis, M. Machedon
We consider a large number of Bosons with interaction potential . In earlier papers we considered a set of equations for the condensate and pair excitati…
Pair excitations and the mean field approximation of interacting Bosons, I
M. Grillakis, M. Machedon
In our previous work \cite{GMM1},\cite{GMM2} we introduced a correction to the mean field approximation of interacting Bosons. This correction describes the evolution of pairs of p…
Second-order corrections to mean-field evolution of weakly interacting Bosons, II
M. Grillakis, M. Machedon, D. Margetis
We study the evolution of a N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper I, in which we derived a second-order correction to a mean…