TY  - JOUR
AU  - Chong, J.
AU  - Dong, X.
AU  - Grillakis, M.
AU  - Machedon, M.
AU  - Zhao, Z.
PY  - 2026
TI  - Global Uniform in N Estimates for Solutions of a System of Hartree–Fock–Bogoliubov Type in the Case β < 1
JO  - Peking Mathematical Journal
SN  - 2096-6075
SP  - 1
EP  - 54
VL  - 9
IS  - 1
AB  - 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.
UR  - https://doi.org/10.1007/s42543-024-00089-5
DO  - 10.1007/s42543-024-00089-5