Global well-posedness of 2D incompressible Navier–Stokes–Darcy flow in a type of generalized time-dependent porosity media

Linlin Tan; Bianru Cheng; Linlin Tan; Bianru Cheng

doi:10.3934/era.2024262

Electronic Research Archive

2024, Volume 32, Issue 10: 5649-5681. doi: 10.3934/era.2024262

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Global well-posedness of 2D incompressible Navier–Stokes–Darcy flow in a type of generalized time-dependent porosity media

Linlin Tan ^1,2,
Bianru Cheng ^{1,2
,
,}

1.
School of Mathematics and Center for Nonlinear Studies, Northwest University, Xi'an 710127, China
2.
Shaanxi Key Laboratory of Mathematical Theory and Computation of Fluid Mechanics, Northwest University, Xi'an 710127, China

Received: 04 August 2024 Revised: 30 September 2024 Accepted: 11 October 2024 Published: 16 October 2024

This study investigates the global well-posedness of a coupled Navier–Stokes–Darcy model incorporating the Beavers–Joseph–Saffman–Jones interface boundary condition in two-dimensional Euclidean space. We establish the existence of global strong solutions for the system in both linear and nonlinear cases where porosity depends on pressure. When dealing with the time-dependent porous media, the primary challenge in obtaining closed prior estimates arises from the presence of complex, sharp interfaces. To address this issue, we employ the classical Trace Theorem. Such space-time variable coupled systems are crucial for understanding underground fluid flow.
Citation: Linlin Tan, Bianru Cheng. Global well-posedness of 2D incompressible Navier–Stokes–Darcy flow in a type of generalized time-dependent porosity media[J]. Electronic Research Archive, 2024, 32(10): 5649-5681. doi: 10.3934/era.2024262

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Abstract

This study investigates the global well-posedness of a coupled Navier–Stokes–Darcy model incorporating the Beavers–Joseph–Saffman–Jones interface boundary condition in two-dimensional Euclidean space. We establish the existence of global strong solutions for the system in both linear and nonlinear cases where porosity depends on pressure. When dealing with the time-dependent porous media, the primary challenge in obtaining closed prior estimates arises from the presence of complex, sharp interfaces. To address this issue, we employ the classical Trace Theorem. Such space-time variable coupled systems are crucial for understanding underground fluid flow.

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