不可压缩非牛顿流体的流体-粒子系统和弗拉索夫方程的全局弱解法

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Pei-yu Zhang, Li Fang, Zhen-hua Guo
{"title":"不可压缩非牛顿流体的流体-粒子系统和弗拉索夫方程的全局弱解法","authors":"Pei-yu Zhang,&nbsp;Li Fang,&nbsp;Zhen-hua Guo","doi":"10.1007/s10255-024-1080-0","DOIUrl":null,"url":null,"abstract":"<div><p>The purpose of this work is to investigate the existence and uniqueness of weak solutions to the initial-boundary value problem for a coupled system of an incompressible non-Newtonian fluid and the Vlasov equation. The coupling arises from the acceleration in the Vlasov equation and the drag force in the incompressible viscous non-Newtonian fluid with the stress tensor of a power-law structure for <span>\\(p\\geqslant {11\\over 5}\\)</span>. The main idea of the existence analysis is to reformulate the coupled system by means of a so-called truncation function. The advantage of the new formulation is to control the external force term <span>\\(G=-\\int_\\mathbb{{R}^{d}}(\\mathbf{u}-\\mathbf{v})fd\\mathbf{v}\\ (d=2,3)\\)</span>. The global existence of weak solutions to the reformulated system is shown by using the Faedo-Galerkin method and weak compactness techniques. We further prove the uniqueness of weak solutions to the considered system.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 4","pages":"954 - 978"},"PeriodicalIF":0.9000,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global Weak Solutions to a Fluid-particle System of an Incompressible Non-Newtonian Fluid and the Vlasov Equation\",\"authors\":\"Pei-yu Zhang,&nbsp;Li Fang,&nbsp;Zhen-hua Guo\",\"doi\":\"10.1007/s10255-024-1080-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The purpose of this work is to investigate the existence and uniqueness of weak solutions to the initial-boundary value problem for a coupled system of an incompressible non-Newtonian fluid and the Vlasov equation. The coupling arises from the acceleration in the Vlasov equation and the drag force in the incompressible viscous non-Newtonian fluid with the stress tensor of a power-law structure for <span>\\\\(p\\\\geqslant {11\\\\over 5}\\\\)</span>. The main idea of the existence analysis is to reformulate the coupled system by means of a so-called truncation function. The advantage of the new formulation is to control the external force term <span>\\\\(G=-\\\\int_\\\\mathbb{{R}^{d}}(\\\\mathbf{u}-\\\\mathbf{v})fd\\\\mathbf{v}\\\\ (d=2,3)\\\\)</span>. The global existence of weak solutions to the reformulated system is shown by using the Faedo-Galerkin method and weak compactness techniques. We further prove the uniqueness of weak solutions to the considered system.</p></div>\",\"PeriodicalId\":6951,\"journal\":{\"name\":\"Acta Mathematicae Applicatae Sinica, English Series\",\"volume\":\"40 4\",\"pages\":\"954 - 978\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-11-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"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/s10255-024-1080-0\",\"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/s10255-024-1080-0","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

这项工作的目的是研究不可压缩非牛顿流体和弗拉索夫方程耦合系统的初始边界值问题的弱解的存在性和唯一性。耦合源于Vlasov方程中的加速度和不可压缩粘性非牛顿流体中的阻力,其应力张量为幂律结构(p\geqslant {11\over 5}\)。存在性分析的主要思想是通过所谓的截断函数来重新表述耦合系统。新公式的优势在于控制外力项(G=-\int_\mathbb{R}^{d}}(\mathbf{u}-\mathbf{v})fd\mathbf{v}\ (d=2,3)\ )。通过使用 Faedo-Galerkin 方法和弱致密性技术,我们证明了重构系统弱解的全局存在性。我们进一步证明了所考虑系统弱解的唯一性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Global Weak Solutions to a Fluid-particle System of an Incompressible Non-Newtonian Fluid and the Vlasov Equation

The purpose of this work is to investigate the existence and uniqueness of weak solutions to the initial-boundary value problem for a coupled system of an incompressible non-Newtonian fluid and the Vlasov equation. The coupling arises from the acceleration in the Vlasov equation and the drag force in the incompressible viscous non-Newtonian fluid with the stress tensor of a power-law structure for \(p\geqslant {11\over 5}\). The main idea of the existence analysis is to reformulate the coupled system by means of a so-called truncation function. The advantage of the new formulation is to control the external force term \(G=-\int_\mathbb{{R}^{d}}(\mathbf{u}-\mathbf{v})fd\mathbf{v}\ (d=2,3)\). The global existence of weak solutions to the reformulated system is shown by using the Faedo-Galerkin method and weak compactness techniques. We further prove the uniqueness of weak solutions to the considered system.

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
CiteScore
1.30
自引率
0.00%
发文量
70
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信