弱阻尼广义Boussinesq方程解的整体存在性和时间衰减率

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-07-01 DOI:10.1063/5.0135436

Yinxia Wang, Zehua Luo, Dan Li

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引用次数: 0

摘要

本文研究了一类具有弱阻尼的广义Boussineq方程的初值问题。在初始数据范数适当小的条件下，建立了所有空间维d≥1时全局解及其导数的存在性和时间衰减率。低频初始数据的负Sobolev范数随时间演化而保持不变，提高了全局解的衰减率。该证明是基于能量法和柔性插值技巧，而没有研究相应的线性方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Global existence and time-decay rates of solutions to the generalized Boussinesq equation with weak damping

In this paper, we study the initial value problem for the generalized Boussineq equation with weak damping. The existence and time-decay rates of global solutions and its derivatives are established for all space dimensions d ≥ 1, provided that the norm of the initial data is suitably small. The negative Sobolev norms of the initial data in low frequency are shown to be preserved along time evolution and enhance the decay rates of global solutions. The proof is based on the energy method and flexible interpolation trick without investigating the corresponding linear equation.

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来源期刊

Journal of Mathematical Physics Analysis Geometry PHYSICS, MATHEMATICAL-

CiteScore

0.70

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects: mathematical problems of modern physics; complex analysis and its applications; asymptotic problems of differential equations; spectral theory including inverse problems and their applications; geometry in large and differential geometry; functional analysis, theory of representations, and operator algebras including ergodic theory. The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.