{"title":"Solvability of an Initial–Boundary Value Problem for the Modified Kelvin–Voigt Model with Memory along Fluid Motion Trajectories","authors":"M. V. Turbin, A. S. Ustiuzhaninova","doi":"10.1134/s0012266124020046","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The paper deals with proving the weak solvability of an initial–boundary value problem for\nthe modified Kelvin–Voigt model taking into account memory along the trajectories of motion of\nfluid particles. To this end, we consider an approximation problem whose solvability is established\nwith the use of the Leray–Schauder fixed point theorem. Then, based on a priori estimates, we\nshow that the sequence of solutions of the approximation problem has a subsequence that weakly\nconverges to the solution of the original problem as the approximation parameter tends to zero.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124020046","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The paper deals with proving the weak solvability of an initial–boundary value problem for
the modified Kelvin–Voigt model taking into account memory along the trajectories of motion of
fluid particles. To this end, we consider an approximation problem whose solvability is established
with the use of the Leray–Schauder fixed point theorem. Then, based on a priori estimates, we
show that the sequence of solutions of the approximation problem has a subsequence that weakly
converges to the solution of the original problem as the approximation parameter tends to zero.
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