{"title":"The Problem of the Flow of One Type of Non-Newtonian Fluid through the Boundary of a Multiply Connected Domain","authors":"V. G. Zvyagin, V. P. Orlov","doi":"10.1134/S1064562423700722","DOIUrl":null,"url":null,"abstract":"<p>The existence of a weak solution of the initial boundary value problem for the equations of motion of a viscoelastic non-Newtonian fluid in a multiply connected domain with memory along trajectories of a nonsmooth velocity field and with an inhomogeneous boundary condition is established. The study assumes Galerkin-type approximations of the original problem followed by passage to the limit based on a priori estimates. The theory of regular Lagrangian flows is used to study the behavior of trajectories of a nonsmooth velocity field.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"107 2","pages":"112 - 116"},"PeriodicalIF":0.5000,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562423700722","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The existence of a weak solution of the initial boundary value problem for the equations of motion of a viscoelastic non-Newtonian fluid in a multiply connected domain with memory along trajectories of a nonsmooth velocity field and with an inhomogeneous boundary condition is established. The study assumes Galerkin-type approximations of the original problem followed by passage to the limit based on a priori estimates. The theory of regular Lagrangian flows is used to study the behavior of trajectories of a nonsmooth velocity field.
期刊介绍：
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
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