Homogenization of Evolutionary Incompressible Navier–Stokes System in Perforated Domains

In this paper, we consider the homogenization problems for evolutionary incompressible Navier–Stokes system in three dimensional domains perforated with a large number of small holes which are periodically located. We first establish certain uniform estimates for the weak solutions. To overcome the...

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Bibliographic Details
Published inJournal of mathematical fluid mechanics Vol. 25; no. 1
Main Authors Lu, Yong, Yang, Peikang
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2023
Springer Nature B.V
Subjects
Classical and Continuum Physics
Domains
Fluid flow
Fluid mechanics
Fluid- and Aerodynamics
Homogenization
In memory of Antonin Novotny
Mathematical analysis
Mathematical Methods in Physics
Navier-Stokes equations
Physics
Physics and Astronomy
Theoretical mathematics
perforated domains
Homogenization
Evolutionary incompressible Navier–Stokes equations
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Summary:In this paper, we consider the homogenization problems for evolutionary incompressible Navier–Stokes system in three dimensional domains perforated with a large number of small holes which are periodically located. We first establish certain uniform estimates for the weak solutions. To overcome the extra difficulties coming from the time derivative, we use the idea of Temam (Navier–Stokes equations, North-Holland, Amsterdam, 1979) and consider the equations by integrating in time variable. After suitably extending the weak solutions to the whole domain, we employ the generalized cell problem to study the limit process.
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ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-022-00745-9