@article{Chong2026, 
author = {J. Chong and X. Dong and M. Grillakis and M. Machedon and Z. Zhao},
title = {Global Uniform in N Estimates for Solutions of a System of Hartree–Fock–Bogoliubov Type in the Case β < 1},
year = {2026},
journal = {Peking Mathematical Journal},
volume = {9},
number = {1},
pages = {1-54},
keywords = {The Hartree–Fock–Bogoliubov System, Mean-field equations},
url = {https://www.sciopen.com/article/10.1007/s42543-024-00089-5},
doi = {10.1007/s42543-024-00089-5},
abstract = {We extend the results of [Commun. Partial. Differ. Equ. 44(12), 1431–1465 (2019)] by the third and fourth author globally in time. More precisely, we prove uniform-in-N Strichartz estimates for the solutions    ϕ,    Λ and    Γ of a coupled system of Hartree–Fock–Bogoliubov type with interaction potential        V    N    (  x  −  y  )  =      N          3      β        v  (      N          β        (  x  −  y  )  ) for    β  <  1. The potential v satisfies some technical conditions, but is not small. The initial conditions have finite energy and the “pair correlation” part satisfies a smallness condition, but are otherwise general functions in suitable Sobolev spaces, and the expected correlations in    Λ develop dynamically in time. The estimates are expected to improve the Fock space bounds of [Ann. Henri Poincaré 23(2), 615–673 (2021)] by the first and fifth author. This will be addressed in a subsequent paper.}
}