{"title":"Analytical and numerical investigation of unsteady flow near a critical point","authors":"A.G. Petrova , V.V. Pukhnachev , O.A. Frolovskaya","doi":"10.1016/j.jappmathmech.2016.07.003","DOIUrl":null,"url":null,"abstract":"<div><p><span>The problem of unsteady flow<span> of a viscous incompressible fluid<span><span> near a critical point on a plane boundary is investigated. A theorem on the existence and uniqueness of its solution in Hölder classes of functions on an arbitrary time interval with natural restrictions imposed on the initial function is proved. Qualitative properties of the solution are investigated. Results of a </span>numerical analysis demonstrating the possibility of disappearance after a finite time of a </span></span></span>counterflow<span> zone existing at the initial time in the case of a negative pressure gradient at the rigid plane are presented. In the case when the pressure gradient is a periodic function, a periodic mode of motion as well as breakdown of the solution after a finite time is possible.</span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"80 3","pages":"Pages 215-224"},"PeriodicalIF":0.0000,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2016.07.003","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Pmm Journal of Applied Mathematics and Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021892816300909","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 11
Abstract
The problem of unsteady flow of a viscous incompressible fluid near a critical point on a plane boundary is investigated. A theorem on the existence and uniqueness of its solution in Hölder classes of functions on an arbitrary time interval with natural restrictions imposed on the initial function is proved. Qualitative properties of the solution are investigated. Results of a numerical analysis demonstrating the possibility of disappearance after a finite time of a counterflow zone existing at the initial time in the case of a negative pressure gradient at the rigid plane are presented. In the case when the pressure gradient is a periodic function, a periodic mode of motion as well as breakdown of the solution after a finite time is possible.
期刊介绍：
This journal is a cover to cover translation of the Russian journal Prikladnaya Matematika i Mekhanika, published by the Russian Academy of Sciences and reflecting all the major achievements of the Russian School of Mechanics.The journal is concerned with high-level mathematical investigations of modern physical and mechanical problems and reports current progress in this field. Special emphasis is placed on aeronautics and space science and such subjects as continuum mechanics, theory of elasticity, and mathematics of space flight guidance and control.
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