n 维不可压缩纳维-斯托克斯方程全局弱解的所有阶衍生物的精确极限和改进衰减估计值

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-04-19 DOI:10.1007/s10255-024-1070-2

Ling-hai Zhang

{"title":"n 维不可压缩纳维-斯托克斯方程全局弱解的所有阶衍生物的精确极限和改进衰减估计值","authors":"Ling-hai Zhang","doi":"10.1007/s10255-024-1070-2","DOIUrl":null,"url":null,"abstract":"<div><p>We couple together existing ideas, existing results, special structure and novel ideas to accomplish the exact limits and improved decay estimates with sharp rates for all order derivatives of the global weak solutions of the Cauchy problem for an <i>n</i>-dimensional incompressible Navier-Stokes equations. We also use the global smooth solution of the corresponding heat equation to approximate the global weak solutions of the incompressible Navier-Stokes equations.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 1","pages":"27 - 83"},"PeriodicalIF":0.9000,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10255-024-1070-2.pdf","citationCount":"0","resultStr":"{\"title\":\"The Exact Limits and Improved Decay Estimates for All Order Derivatives of the Global Weak Solutions of n-Dimensional Incompressible Navier-Stokes Equations\",\"authors\":\"Ling-hai Zhang\",\"doi\":\"10.1007/s10255-024-1070-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We couple together existing ideas, existing results, special structure and novel ideas to accomplish the exact limits and improved decay estimates with sharp rates for all order derivatives of the global weak solutions of the Cauchy problem for an <i>n</i>-dimensional incompressible Navier-Stokes equations. We also use the global smooth solution of the corresponding heat equation to approximate the global weak solutions of the incompressible Navier-Stokes equations.</p></div>\",\"PeriodicalId\":6951,\"journal\":{\"name\":\"Acta Mathematicae Applicatae Sinica, English Series\",\"volume\":\"41 1\",\"pages\":\"27 - 83\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-04-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10255-024-1070-2.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematicae Applicatae Sinica, English Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10255-024-1070-2\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematicae Applicatae Sinica, English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10255-024-1070-2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

我们将现有思想、现有结果、特殊结构和新颖思想结合起来，完成了 n 维不可压缩纳维-斯托克斯方程的考希问题全局弱解的精确极限和改进的衰减估计，并具有尖锐的衰减率。我们还利用相应热方程的全局平稳解来近似不可压缩 Navier-Stokes 方程的全局弱解。

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

The Exact Limits and Improved Decay Estimates for All Order Derivatives of the Global Weak Solutions of n-Dimensional Incompressible Navier-Stokes Equations

We couple together existing ideas, existing results, special structure and novel ideas to accomplish the exact limits and improved decay estimates with sharp rates for all order derivatives of the global weak solutions of the Cauchy problem for an n-dimensional incompressible Navier-Stokes equations. We also use the global smooth solution of the corresponding heat equation to approximate the global weak solutions of the incompressible Navier-Stokes equations.

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

Acta Mathematicae Applicatae Sinica, English Series 数学-应用数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.