Existence and uniqueness of time-periodic solutions to the Oberbeck–Boussinesq system

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2025-07-29 DOI:10.1016/j.nonrwa.2025.104461

Tomoyuki Nakatsuka

引用次数: 0

Abstract

This paper is devoted to the study of the time-periodic problem for the Oberbeck–Boussinesq system in the whole space. Our investigation is based on the reformulation of the time-periodic problem and does not depend on the analysis of the initial value problem. We construct a time-periodic solution with more information on its structure than the solutions in preceding studies. We also prove that our solution, small in an appropriate sense, is unique in the class of solutions having slightly more regularity.

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Oberbeck-Boussinesq系统时间周期解的存在唯一性

本文研究了全空间上的Oberbeck-Boussinesq系统的时间周期问题。我们的研究是基于时间周期问题的重新表述，而不依赖于对初值问题的分析。我们构造了一个具有更多结构信息的时间周期解。我们也证明了我们的解，在适当的意义上是小的，在有更多正则性的解的类别中是唯一的。

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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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.