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Volume 18, Issue 5
Global Well-Posedness for Navier-Stokes-Darcy Equations with the Free Interface

Bin Zhao, Mingyue Zhang & Chuangchuang Liang

Int. J. Numer. Anal. Mod., 18 (2021), pp. 569-619.

Published online: 2021-08

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  • Abstract

In this paper, the Navier-Stokes-Darcy equations with the free interface are considered, which model the movement of the sea and the sand in the seafloor or the filtration of blood through the arterial wall. The global well-posedness of the solution perturbed around the constant steady state is obtained and then the almost exponential decay to the constant stationary state is gained. Finally, we present an efficient explicit discrete scheme based on finite-volume method for the free interface system and provide the numerical tests to illustrate the consistency with our analysis result.

  • Keywords

Navier-Stokes-Darcy equations, the free interface, global well-posedness, large time behavior.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-18-569, author = {Zhao , BinZhang , Mingyue and Liang , Chuangchuang}, title = {Global Well-Posedness for Navier-Stokes-Darcy Equations with the Free Interface}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2021}, volume = {18}, number = {5}, pages = {569--619}, abstract = {

In this paper, the Navier-Stokes-Darcy equations with the free interface are considered, which model the movement of the sea and the sand in the seafloor or the filtration of blood through the arterial wall. The global well-posedness of the solution perturbed around the constant steady state is obtained and then the almost exponential decay to the constant stationary state is gained. Finally, we present an efficient explicit discrete scheme based on finite-volume method for the free interface system and provide the numerical tests to illustrate the consistency with our analysis result.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/19384.html} }
TY - JOUR T1 - Global Well-Posedness for Navier-Stokes-Darcy Equations with the Free Interface AU - Zhao , Bin AU - Zhang , Mingyue AU - Liang , Chuangchuang JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 569 EP - 619 PY - 2021 DA - 2021/08 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/19384.html KW - Navier-Stokes-Darcy equations, the free interface, global well-posedness, large time behavior. AB -

In this paper, the Navier-Stokes-Darcy equations with the free interface are considered, which model the movement of the sea and the sand in the seafloor or the filtration of blood through the arterial wall. The global well-posedness of the solution perturbed around the constant steady state is obtained and then the almost exponential decay to the constant stationary state is gained. Finally, we present an efficient explicit discrete scheme based on finite-volume method for the free interface system and provide the numerical tests to illustrate the consistency with our analysis result.

Zhao , BinZhang , Mingyue and Liang , Chuangchuang. (2021). Global Well-Posedness for Navier-Stokes-Darcy Equations with the Free Interface. International Journal of Numerical Analysis and Modeling. 18 (5). 569-619. doi:
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