New lower bounds on the radius of spatial analyticity for the higher order nonlinear dispersive equation on the real line

IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Zaiyun Zhang, Youjun Deng, Xinping Li
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引用次数: 0

Abstract

In this paper, benefited some ideas of Wang [J. Geom. Anal. 33, 18 (2023)] and Dufera et al. [J. Math. Anal. Appl. 509, 126001 (2022)], we investigate persistence of spatial analyticity for solution of the higher order nonlinear dispersive equation with the initial data in modified Gevrey space. More precisely, using the contraction mapping principle, the bilinear estimate as well as approximate conservation law, we establish the persistence of the radius of spatial analyticity till some time δ. Then, given initial data that is analytic with fixed radius σ0, we obtain asymptotic lower bound σ(t)≥c|t|−12, for large time t ≥ δ. This result improves earlier ones in the literatures, such as Zhang et al. [Discrete Contin. Dyn. Syst. B 29, 937–970 (2024)], Huang–Wang [J. Differ. Equations 266, 5278–5317 (2019)], Liu–Wang [Nonlinear Differ. Equations Appl. 29, 57 (2022)], Wang [J. Geom. Anal. 33, 18 (2023)] and Selberg–Tesfahun [Ann. Henri Poincaré 18, 3553–3564 (2017)].
实线上高阶非线性色散方程空间解析性半径的新下限
本文借鉴王文[J. Geom. Anal. 33, 18 (2023)]和杜费拉等人[J. Math. Anal. Appl. 509, 126001 (2022)]的一些观点,研究了高阶非线性色散方程在修正 Gevrey 空间中初始数据的空间解析性的持久性。更确切地说,利用收缩映射原理、双线性估计以及近似守恒定律,我们确定了空间解析性半径在某个时间 δ 之前的持久性。然后,给定初始数据为具有固定半径 σ0 的解析性数据,我们得到了大时间 t ≥ δ 时的渐近下界 σ(t)≥c|t|-12。这一结果改进了早期文献中的结果,如 Zhang 等人 [Discrete Contin.方程 266, 5278-5317 (2019)], Liu-Wang [Nonlinear Differ. Equations Appl. 29, 57 (2022)], Wang [J. Geom. Anal. 33, 18 (2023)] and Selberg-Tesfahun [Ann. Henri Poincaré 18, 3553-3564 (2017)].
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来源期刊
Journal of Mathematical Physics
Journal of Mathematical Physics 物理-物理:数学物理
CiteScore
2.20
自引率
15.40%
发文量
396
审稿时长
4.3 months
期刊介绍: Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.
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