Analysis of the Brinkman-Forchheimer equations with slip boundary conditions

TL;DR

This paper investigates the Brinkman-Forchheimer equations with slip boundary conditions, establishing existence, uniqueness, stability, and coefficient dependence of weak solutions through mathematical analysis.

Contribution

It provides new proofs for existence and uniqueness of solutions, analyzes their stability, and explores the effect of coefficients on solutions for these equations.

Findings

Existence and uniqueness of weak solutions proven.

Solution stability under stationary conditions demonstrated.

Continuity of solutions with respect to model coefficients established.

Abstract

In this work, we study the Brinkman-Forchheimer equations driven under slip boundary conditions of friction type. We prove the existence and uniqueness of weak solutions by means of regularization combined with the Faedo-Galerkin approach. Next we discuss the continuity of the solution with respect to Brinkman's and Forchheimer's coefficients. Finally, we show that the weak solution of the corresponding stationary problem is stable.