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

Yan Ren Hou; Dan Dan Xue; Yao Lin Jiang

doi:10.1007/s10114-022-9134-9

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

Yan Ren Hou
, Dan Dan Xue
, Yao Lin Jiang

数学与统计学院

Xi'an Jiaotong University
Xinjiang University
Chengdu University of Technology

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	939-951
页数	13
期刊	Acta Mathematica Sinica, English Series
卷	39
期	5
DOI	https://doi.org/10.1007/s10114-022-9134-9
出版状态	已出版 - 5月 2023

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title = "On the Weak Solutions to Steady-State Mixed Navier—Stokes/Darcy Model",

abstract = "In this paper, for the mixed Navier—Stokes/Darcy model with Beavers—Joseph—Saffman{\textquoteright}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.",

keywords = "76D03, 76D05, 76S05, Navier—Stokes equations, Porous media flow, a priori estimate, existence and global uniqueness, weak solution",

author = "Hou, \{Yan Ren\} and Xue, \{Dan Dan\} and Jiang, \{Yao Lin\}",

note = "Publisher Copyright: {\textcopyright} 2022, Springer-Verlag GmbH Germany \& The Editorial Office of AMS.",

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doi = "10.1007/s10114-022-9134-9",

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T1 - On the Weak Solutions to Steady-State Mixed Navier—Stokes/Darcy Model

AU - Hou, Yan Ren

AU - Xue, Dan Dan

AU - Jiang, Yao Lin

PY - 2023/5

Y1 - 2023/5

N2 - 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.

AB - 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.

KW - 76D03

KW - 76D05

KW - 76S05

KW - Navier—Stokes equations

KW - Porous media flow

KW - a priori estimate

KW - existence and global uniqueness

KW - weak solution

UR - https://www.scopus.com/pages/publications/85138196460

U2 - 10.1007/s10114-022-9134-9

DO - 10.1007/s10114-022-9134-9

M3 - 文章

AN - SCOPUS:85138196460

SN - 1439-8516

VL - 39

SP - 939

EP - 951

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 5

ER -

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

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