An approach to the global well-posedness of a coupled 3-dimensional Navier-Stokes-Darcy model with Beavers-Joseph-Saffman-Jones interface boundary condition

Linlin Tan; Meiying Cui; Bianru Cheng; Linlin Tan; Meiying Cui; Bianru Cheng

doi:10.3934/math.2024341

AIMS Mathematics

2024, Volume 9, Issue 3: 6993-7016. doi: 10.3934/math.2024341

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An approach to the global well-posedness of a coupled 3-dimensional Navier-Stokes-Darcy model with Beavers-Joseph-Saffman-Jones interface boundary condition

1.
School of Mathematics and Center for Nonlinear Studies, Northwest University, Xi'an, 710127, China
2.
School of Mathematics and Statistics, Yulin University, Yulin, 719000, China

Received: 06 January 2024 Revised: 01 February 2024 Accepted: 05 February 2024 Published: 19 February 2024
MSC : 35A07, 74F10, 76D03, 76N10

This study focused on investigating the global well-posedness of a coupled Navier-Stokes-Darcy model with the Beavers-Joseph-Saffman-Jones interface boundary condition in the three-dimensional Euclidean space. By utilizing this approach, we successfully obtained the global strong solution of the system in the three-dimensional space. Furthermore, we demonstrated the exponential stability of this strong solution. The significance of such coupled systems lies in their pivotal role in the analysis of subsurface flow problems, particularly in the context of karst aquifers.
- global well-posedness,
- Navier-Stokes-Darcy model,
- Beavers-Joseph-Saffman-Jones interface boundary condition,
- large time behavior,
- exponential stability
Citation: Linlin Tan, Meiying Cui, Bianru Cheng. An approach to the global well-posedness of a coupled 3-dimensional Navier-Stokes-Darcy model with Beavers-Joseph-Saffman-Jones interface boundary condition[J]. AIMS Mathematics, 2024, 9(3): 6993-7016. doi: 10.3934/math.2024341

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Abstract

This study focused on investigating the global well-posedness of a coupled Navier-Stokes-Darcy model with the Beavers-Joseph-Saffman-Jones interface boundary condition in the three-dimensional Euclidean space. By utilizing this approach, we successfully obtained the global strong solution of the system in the three-dimensional space. Furthermore, we demonstrated the exponential stability of this strong solution. The significance of such coupled systems lies in their pivotal role in the analysis of subsurface flow problems, particularly in the context of karst aquifers.

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