On the Weak Solutions to Mixed Navier-Stokes-Darcy Model

TL;DR

This paper establishes the existence, a priori estimates, and global uniqueness of weak solutions to the mixed Navier-Stokes-Darcy model with interface conditions, without restrictions on data size or viscosity.

Contribution

It provides the first proof of existence and uniqueness of weak solutions for the model without small data or large viscosity assumptions.

Findings

Existence of weak solutions established

A priori estimates derived

Global uniqueness proved

Abstract

In this paper, an a priori estimate of weak solutions to the mixed Navier-Stokes/Darcy model with Beavers-Joseph-Saffman's interface condition and the existence of a weak solution are established without the small data and/or the large viscosity restriction for the first time. Based on these results, the global uniqueness of the weak solution is obtained.