不可压缩Navier-Stokes流大时间特性的抛物标度

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2025-03-04 DOI:10.1016/j.nonrwa.2025.104350

Masakazu Yamamoto

{"title":"不可压缩Navier-Stokes流大时间特性的抛物标度","authors":"Masakazu Yamamoto","doi":"10.1016/j.nonrwa.2025.104350","DOIUrl":null,"url":null,"abstract":"<div><div>Through asymptotic expansion, the large-time behavior of incompressible Navier–Stokes flow in <span><math><mi>n</mi></math></span>-dimensional whole space is depicted. Especially, from their parabolic scalings, large-time behaviors of any terms on the expansion are clarified. The parabolic scalings also guarantee the uniqueness of the expansion. In the preceding work, the expansion with the <span><math><mi>n</mi></math></span>th order has already been derived. They also predicted that the flow has some logarithmic evolutions in higher-order decay. In this paper, an asymptotic expansion with <span><math><mrow><mn>2</mn><mi>n</mi></mrow></math></span>th order is presented. Furthermore, logarithmic evolutions are discovered.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104350"},"PeriodicalIF":1.8000,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Parabolic-scalings on large-time behavior of the incompressible Navier–Stokes flow\",\"authors\":\"Masakazu Yamamoto\",\"doi\":\"10.1016/j.nonrwa.2025.104350\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Through asymptotic expansion, the large-time behavior of incompressible Navier–Stokes flow in <span><math><mi>n</mi></math></span>-dimensional whole space is depicted. Especially, from their parabolic scalings, large-time behaviors of any terms on the expansion are clarified. The parabolic scalings also guarantee the uniqueness of the expansion. In the preceding work, the expansion with the <span><math><mi>n</mi></math></span>th order has already been derived. They also predicted that the flow has some logarithmic evolutions in higher-order decay. In this paper, an asymptotic expansion with <span><math><mrow><mn>2</mn><mi>n</mi></mrow></math></span>th order is presented. Furthermore, logarithmic evolutions are discovered.</div></div>\",\"PeriodicalId\":49745,\"journal\":{\"name\":\"Nonlinear Analysis-Real World Applications\",\"volume\":\"85 \",\"pages\":\"Article 104350\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2025-03-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis-Real World Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1468121825000367\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121825000367","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

通过渐近展开，刻画了n维整体空间中不可压缩Navier-Stokes流的大时态。特别地，从它们的抛物标度出发，阐明了任意项在展开式上的大时性质。抛物线标量也保证了展开式的唯一性。在前面的工作中，已经导出了n阶展开式。他们还预测，该流在高阶衰减中有一些对数演化。本文给出了一个二阶渐近展开式。此外，还发现了对数演化。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Parabolic-scalings on large-time behavior of the incompressible Navier–Stokes flow

Through asymptotic expansion, the large-time behavior of incompressible Navier–Stokes flow in

n

-dimensional whole space is depicted. Especially, from their parabolic scalings, large-time behaviors of any terms on the expansion are clarified. The parabolic scalings also guarantee the uniqueness of the expansion. In the preceding work, the expansion with the

n

th order has already been derived. They also predicted that the flow has some logarithmic evolutions in higher-order decay. In this paper, an asymptotic expansion with

2 n

th order is presented. Furthermore, logarithmic evolutions are discovered.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.