Global estimates for the Hartree–Fock–Bogoliubov equations

Jacky Chong; Manoussos Grillakis; Matei Machedon; Zehua Zhao

doi:10.1080/03605302.2021.1920615

Global estimates for the Hartree–Fock–Bogoliubov equations

Jacky Chong
, Manoussos Grillakis
, Matei Machedon^*
, Zehua Zhao

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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 (Formula presented.) in mixed coordinates such as (Formula presented.) (Formula presented.) (Formula presented.) The main new technical ingredient is a dispersive estimate in mixed coordinates, which may be of interest in its own right.

Original language	English
Pages (from-to)	2015-2055
Number of pages	41
Journal	Communications in Partial Differential Equations
Volume	46
Issue number	10
DOIs	https://doi.org/10.1080/03605302.2021.1920615
Publication status	Published - 2021
Externally published	Yes

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Keywords

Dispersive estimates; Hartree–Fock–Bogoliubov; Strichartz estimates

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10.1080/03605302.2021.1920615

Cite this

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title = "Global estimates for the Hartree–Fock–Bogoliubov equations",

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 (Formula presented.) in mixed coordinates such as (Formula presented.) (Formula presented.) (Formula presented.) The main new technical ingredient is a dispersive estimate in mixed coordinates, which may be of interest in its own right.",

keywords = "Dispersive estimates; Hartree–Fock–Bogoliubov; Strichartz estimates",

author = "Jacky Chong and Manoussos Grillakis and Matei Machedon and Zehua Zhao",

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year = "2021",

doi = "10.1080/03605302.2021.1920615",

language = "English",

volume = "46",

pages = "2015--2055",

journal = "Communications in Partial Differential Equations",

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TY - JOUR

T1 - Global estimates for the Hartree–Fock–Bogoliubov equations

AU - Chong, Jacky

AU - Grillakis, Manoussos

AU - Machedon, Matei

AU - Zhao, Zehua

PY - 2021

Y1 - 2021

N2 - 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 (Formula presented.) in mixed coordinates such as (Formula presented.) (Formula presented.) (Formula presented.) The main new technical ingredient is a dispersive estimate in mixed coordinates, which may be of interest in its own right.

AB - 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 (Formula presented.) in mixed coordinates such as (Formula presented.) (Formula presented.) (Formula presented.) The main new technical ingredient is a dispersive estimate in mixed coordinates, which may be of interest in its own right.

KW - Dispersive estimates; Hartree–Fock–Bogoliubov; Strichartz estimates

UR - https://www.scopus.com/pages/publications/85106005390

U2 - 10.1080/03605302.2021.1920615

DO - 10.1080/03605302.2021.1920615

M3 - Article

AN - SCOPUS:85106005390

SN - 0360-5302

VL - 46

SP - 2015

EP - 2055

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 10

ER -

Global estimates for the Hartree–Fock–Bogoliubov equations

Abstract

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Keywords

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