周期\(\mathrm{L}_{p}\)的有界性估计:在Navier-Stokes方程上的应用

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Acta Applicandae Mathematicae Pub Date : 2023-10-16 DOI:10.1007/s10440-023-00612-3

Thomas Eiter, Mads Kyed, Yoshihiro Shibata

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引用次数: 1

摘要

研究了Banach空间中的一般演化方程。基于de Leeuw转移原理的算子值版本，时间周期\（\mathrm{L}_{p} \）最大正则性类型的估计从ℛ-解算子族的界(ℛ-求解器）到相应的预解决问题。利用该方法，在两种配置下，Navier-Stokes方程的时间周期解的存在性得到了证明：在周期移动的有界域中和在外部域中，受规定的时间周期强迫和边界数据的影响。

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Periodic \(\mathrm{L}_{p}\) Estimates by ℛ-Boundedness: Applications to the Navier-Stokes Equations

General evolution equations in Banach spaces are investigated. Based on an operator-valued version of de Leeuw’s transference principle, time-periodic \(\mathrm {L}_{p}\) estimates of maximal regularity type are carried over from ℛ-bounds of the family of solution operators (ℛ-solvers) to the corresponding resolvent problems. With this method, existence of time-periodic solutions to the Navier-Stokes equations is shown for two configurations: in a periodically moving bounded domain and in an exterior domain, subject to prescribed time-periodic forcing and boundary data.

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来源期刊

Acta Applicandae Mathematicae 数学-应用数学

CiteScore

2.80

自引率

6.20%

发文量

审稿时长

16.2 months

期刊介绍： Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.