Sharp convergence rates for Darcy’s law

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Abstract

This article is concerned with Darcy’s law for an incompressible viscous fluid flowing in a porous medium. We establish the sharp (Formula presented.) convergence rate in a periodically perforated and bounded domain in (Formula presented.) for (Formula presented.) where ε represents the size of solid obstacles. This is achieved by constructing two boundary layer correctors to control the boundary layers created by the incompressibility condition and the discrepancy of boundary values between the solution and the leading term in its asymptotic expansion. One of the correctors deals with the tangential boundary data, while the other handles the normal boundary data.

Original languageEnglish
Pages (from-to)1098-1123
Number of pages26
JournalCommunications in Partial Differential Equations
Volume47
Issue number6
DOIs
StatePublished - 2022

Bibliographical note

Funding Information:
This article was supported in part by NSF grant DMS-1856235 and by Simons Fellowship. The author thanks Jinping Zhuge for several valuable comments. The author is also grateful for the valuable suggestions and corrections made by the anonymous referees.

Publisher Copyright:
© 2022 Taylor & Francis Group, LLC.

Keywords

  • Darcy’s Law
  • convergence rate
  • stokes equations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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