{"title":"Investigation of Weak Solvability of One Model Nonlinear Viscosity Fluid","authors":"E. I. Kostenko","doi":"10.1134/s199508022460119x","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper is devoted to investigating the weak solvability of one model nonlinear viscosity fluid motion with memory along the trajectories of fluid particles determined by the velocity field. We used the topological approximation method for studying hydrodynamic problems, the theory of regular Lagrangian flow, when proving the solvability of the described model. The existence of at least one weak solution of the nonlinear viscosity fluid is proved in the paper.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"37 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s199508022460119x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is devoted to investigating the weak solvability of one model nonlinear viscosity fluid motion with memory along the trajectories of fluid particles determined by the velocity field. We used the topological approximation method for studying hydrodynamic problems, the theory of regular Lagrangian flow, when proving the solvability of the described model. The existence of at least one weak solution of the nonlinear viscosity fluid is proved in the paper.
期刊介绍：
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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