{"title":"On buoyancy‐driven viscous incompressible flows with various types of boundary conditions","authors":"M. Beneš, P. Kučera, Petra Vacková","doi":"10.1002/zamm.202200529","DOIUrl":null,"url":null,"abstract":"In this paper, we study the existence and uniqueness of solutions to the initial‐boundary‐value problem for time‐dependent flows of heat‐conducting incompressible fluids through the two‐dimensional channel. The boundary conditions are of two types: the so‐called “do nothing” boundary condition on the outflow and the so‐called Navier boundary conditions on the solid walls of the channel. A priori estimates play a crucial role in existential analysis, however, the considered mixed boundary conditions do not enable us to derive an energy‐type estimate of the solution. Our aim is to prove the existence and uniqueness of a solution on a sufficiently short time interval for arbitrarily large data.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1002/zamm.202200529","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, we study the existence and uniqueness of solutions to the initial‐boundary‐value problem for time‐dependent flows of heat‐conducting incompressible fluids through the two‐dimensional channel. The boundary conditions are of two types: the so‐called “do nothing” boundary condition on the outflow and the so‐called Navier boundary conditions on the solid walls of the channel. A priori estimates play a crucial role in existential analysis, however, the considered mixed boundary conditions do not enable us to derive an energy‐type estimate of the solution. Our aim is to prove the existence and uniqueness of a solution on a sufficiently short time interval for arbitrarily large data.
期刊介绍:
ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.