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

被引：0

作者：

Cacciafesta, Federico ^{[1
]}

de Suzzoni, Anne-Sophie ^{[2
]}

Meng, Long ^{[3
]}

Sok, Jeremy ^{[1
]}

机构：

[1] Univ Padua, Dipartimento Matemat, Via Trieste 63, I-35131 Padua, PD, Italy

[2] Univ Paris Saclay, Ecole Polytech, CMLS, CNRS, F-91128 Palaiseau, France

[3] Ecole ponts ParisTech, CERMICS, 6 & 8 Ave, F-77455 Marne La Vallee, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2024年 / 239卷

基金：

欧洲研究理事会;

关键词：

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

D O I：

10.1016/j.na.2023.113420

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (c) 2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

引用

页数：33

共 50 条

[1] On global well-posedness and scattering for the massive Dirac-Klein-Gordon system
Bejenaru, Ioan
Herr, Sebastian
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2017, 19 (08) : 2445 - 2467
[2] LOW REGULARITY WELL-POSEDNESS FOR THE ONE-DIMENSIONAL DIRAC-KLEIN-GORDON SYSTEM
Pecher, Hartmut
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2006,
[3] Modified low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system
Pecher, Hartmut
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2008, 15 (03): : 279 - 294
[4] Modified low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system
Hartmut Pecher
Nonlinear Differential Equations and Applications NoDEA, 2008, 15 : 279 - 294
[5] Low regularity well-posedness of the Dirac-Klein-Gordon equations in one space dimension
Selberg, Sigmund
Tesfahun, Achenef
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2008, 10 (02) : 181 - 194
[6] LOW REGULARITY AND LOCAL WELL-POSEDNESS FOR THE 1+3 DIMENSIONAL DIRAC-KLEIN-GORDON SYSTEM
Tesfahun, Achenef
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2007,
[7] Global Well-posedness Below the Charge Norm for the Dirac-Klein-Gordon System in One Space Dimension
Selberg, Sigmund
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2007, 2007
[8] Local well-posedness below the charge norm for the Dirac-Klein-Gordon system in two space dimensions
D'Ancona, Piero
Foschi, Damiano
Selberg, Sigmund
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2007, 4 (02) : 295 - 330
[9] GLOBAL WELL-POSEDNESS OF THE 1D DIRAC-KLEIN-GORDON SYSTEM IN SOBOLEV SPACES OF NEGATIVE INDEX
Tesfahun, Achenef
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2009, 6 (03) : 631 - 661
[10] Remarks on ill-posedness for the Dirac-Klein-Gordon system
Machihara, Shuji
Okamoto, Mamoru
DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS, 2016, 13 (03) : 179 - 190

← 1 2 3 4 5 →