On the solution of the coupled steady-state dual-porosity-Navier-Stokes fluid flow model with the Beavers-Joseph-Saffman interface condition

TL;DR

This paper introduces a new analysis method for a coupled dual-porosity-Navier-Stokes model with Beavers-Joseph-Saffman interface, providing a priori estimates and existence results independent of data size or viscosity, ensuring global uniqueness.

Contribution

The paper presents a novel analysis strategy that guarantees a priori estimates and existence of solutions without restrictions on data size or viscosity, leading to global uniqueness.

Findings

Established an a priori estimate for weak solutions.

Proved existence of solutions independent of data size.

Achieved global uniqueness of the weak solution.

Abstract

In this work, we propose a new analysis strategy to establish an a priori estimate of the weak solutions to the coupled steady-state dual-porosity-Navier-Stokes fluid flow model with the Beavers-Joseph-Saffman interface condition. The most advantage of our proposed method is that the a priori estimate and the existence result are independent of small data and the large viscosity restriction. Therefore the global uniqueness of the weak solution is naturally obtained.