一维Dirac-Klein-Gordon系统解的高Sobolev范数随时间的增长

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2019-08-21 DOI:10.1142/S0219891619500127

Achenef Tesfahun

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引用次数: 2

摘要

研究一维Dirac-Klein-Gordon (DKG)方程解的高阶Sobolev范数随时间的增长。我们证明这些范数最多以多项式随时间增长。证明的主要成分是由Colliander, Keel, Staffilani, Takaoka和Tao引入的倒立[公式:见文本]方法，以及双线性零形式估计。

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Growth-in-time of higher Sobolev norms of solutions to the 1D Dirac–Klein–Gordon system

We study the growth-in-time of higher order Sobolev norms of solutions to the Dirac–Klein–Gordon (DKG) equations in one space dimension. We show that these norms grow at most polynomially-in-time. The main ingredients in the proof are the upside-down [Formula: see text]-method which was introduced by Colliander, Keel, Staffilani, Takaoka and Tao, and bilinear null-form estimates.

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来源期刊

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.