几何流自相似解的稳定性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-05-30 DOI:10.4171/ifb/488

Hengrong Du, Nung Kwan Yip

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引用次数: 0

摘要

我们证明了整个图的平均曲率流、表面扩散流和Willmore流的自相似解在具有小Lipschitz范数的初始数据扰动下是稳定的。粗略地说，当时间趋于无穷时，摄动解是渐近自相似的。我们的结果建立在Koch和Lamm于2012年构建的全局解析解，Asai和Giga于2014年采用的紧性参数以及某些加权函数空间上的空间等衰减特性的基础上。通过利用线性化算子的估计，在一个统一的框架中实现了上述所有流的证明。

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Stability of self-similar solutions to geometric flows

We show that self-similar solutions for the mean curvature flow, surface diffusion, and Willmore flow of entire graphs are stable upon perturbations of initial data with small Lipschitz norm. Roughly speaking, the perturbed solutions are asymptotically self-similar as time tends to infinity. Our results are built upon the global analytic solutions constructed by Koch and Lamm in 2012, the compactness arguments adapted by Asai and Giga in 2014, and the spatial equi-decay properties on certain weighted function spaces. The proof for all of the above flows are achieved in a unified framework by utilizing the estimates of the linearized operator.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.