On the Weak Solutions to Steady-State Mixed Navier—Stokes/Darcy Model

In this paper, for the mixed Navier—Stokes/Darcy model with Beavers—Joseph—Saffman’s interface condition, we first establish an a priori estimate for possible weak solutions by means of expanding the coupled system. Then we prove the existence of weak solutions without the small data and/or large vi...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 39; no. 5; pp. 939 - 951
Main Authors Hou, Yan Ren, Xue, Dan Dan, Jiang, Yao Lin
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2023
Springer Nature B.V
Subjects
Fluid flow
Interface analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Viscosity
weak solution
76D03
76S05
76D05
Porous media flow
a priori estimate
Navier—Stokes equations
existence and global uniqueness
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Summary:In this paper, for the mixed Navier—Stokes/Darcy model with Beavers—Joseph—Saffman’s interface condition, we first establish an a priori estimate for possible weak solutions by means of expanding the coupled system. Then we prove the existence of weak solutions without the small data and/or large viscosity restriction, which is required for the existence of the weak solutions in literatures. As a direct corollary, we also get the global uniqueness of the weak solution.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-022-9134-9