Large time well-posedness for a Dirac–Klein–Gordon system

Federico Cacciafesta; Anne Sophie de Suzzoni; Long Meng; Jérémy Sok

doi:10.1016/j.na.2023.113420

Large time well-posedness for a Dirac–Klein–Gordon system

Federico Cacciafesta
, Anne Sophie de Suzzoni
, Long Meng
, Jérémy Sok

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

Abstract

In this paper, we prove well-posedness for a Dirac equation perturbed with a moving potential W that satisfies a Klein–Gordon equation. This represents a “toy model” for atoms with relativistic corrections, as the wave function of the electrons interacts with an electric field generated by a nucleus with a given charge density. One of the main ingredients we need is a new family of Strichartz estimates for time-dependent perturbations of the Dirac equation: these represent a result of independent interest.

Original language	English
Article number	113420
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	239
DOIs	https://doi.org/10.1016/j.na.2023.113420
Publication status	Published - 1 Feb 2024
Externally published	Yes

Keywords

Dirac equation
Globall existence
Time-dependent perturbation of the Strichartz estimate

Access to Document

10.1016/j.na.2023.113420

Cite this

@article{bf080313e050432789816b29c36c9bf9,

title = "Large time well-posedness for a Dirac–Klein–Gordon system",

abstract = "In this paper, we prove well-posedness for a Dirac equation perturbed with a moving potential W that satisfies a Klein–Gordon equation. This represents a “toy model” for atoms with relativistic corrections, as the wave function of the electrons interacts with an electric field generated by a nucleus with a given charge density. One of the main ingredients we need is a new family of Strichartz estimates for time-dependent perturbations of the Dirac equation: these represent a result of independent interest.",

keywords = "Dirac equation, Globall existence, Time-dependent perturbation of the Strichartz estimate",

author = "Federico Cacciafesta and \{de Suzzoni\}, \{Anne Sophie\} and Long Meng and J{\'e}r{\'e}my Sok",

note = "Publisher Copyright: {\textcopyright} 2023 The Authors",

year = "2024",

month = feb,

day = "1",

doi = "10.1016/j.na.2023.113420",

language = "English",

volume = "239",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

}

TY - JOUR

T1 - Large time well-posedness for a Dirac–Klein–Gordon system

AU - Cacciafesta, Federico

AU - de Suzzoni, Anne Sophie

AU - Meng, Long

AU - Sok, Jérémy

PY - 2024/2/1

Y1 - 2024/2/1

N2 - In this paper, we prove well-posedness for a Dirac equation perturbed with a moving potential W that satisfies a Klein–Gordon equation. This represents a “toy model” for atoms with relativistic corrections, as the wave function of the electrons interacts with an electric field generated by a nucleus with a given charge density. One of the main ingredients we need is a new family of Strichartz estimates for time-dependent perturbations of the Dirac equation: these represent a result of independent interest.

AB - In this paper, we prove well-posedness for a Dirac equation perturbed with a moving potential W that satisfies a Klein–Gordon equation. This represents a “toy model” for atoms with relativistic corrections, as the wave function of the electrons interacts with an electric field generated by a nucleus with a given charge density. One of the main ingredients we need is a new family of Strichartz estimates for time-dependent perturbations of the Dirac equation: these represent a result of independent interest.

KW - Dirac equation

KW - Globall existence

KW - Time-dependent perturbation of the Strichartz estimate

U2 - 10.1016/j.na.2023.113420

DO - 10.1016/j.na.2023.113420

M3 - Article

AN - SCOPUS:85174976561

SN - 0362-546X

VL - 239

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

M1 - 113420

ER -

Large time well-posedness for a Dirac–Klein–Gordon system

Abstract

Keywords

Access to Document

Fingerprint

Cite this