Global estimates for the Hartree-Fock-Bogoliubov equations

2020/08/04 by Jacky J. Chong, Jacky Jia Wei Chong, Manoussos G. Grillakis +6
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #math.AP

paper · pdf · doi:10.48550/arxiv.2008.01753

arxiv created 2020/08/04 · openalex publication_date 2020/08/04 · arxiv updated 2020/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that certain Sobolev-type norms, slightly stronger than those given by energy conservation, stay bounded uniformly in time and N. This allows one to extend the local existence results of the second and third author globally in time. The proof is based on interaction Morawetz-type estimates and Strichartz estimates (including some new end-point results) for the equation \ (1)/(i)∂_t-Δ_x-Δ_y+(1)/(N)V_N(x-y) \Λ(t, x, y) =F in mixed coordinates such as L^p(dt) L^q(dx) L²(dy), L^p(dt) L^q(dy) L²(dx), L^p(dt) L^q(d(x-y)) L²(d(x+y)). The main new technical ingredient is a dispersive estimate in mixed coordinates, which may be of interest in its own right.

Citations

• Decay estimates for Schrödinger operators

Cited by

• Dynamical Hartree-Fock-Bogoliubov Approximation of Interacting Bosons

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