Analysis of the Brinkman-Forchheimer equations with slip boundary conditions

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.

Keywords:

• Brinkman–Forchheimer equations
• slip boundary conditions
• weak solutions
• continuous dependence
• stability

AMS Subject Classifications:

• 35J85
• 35Q30
• 76D03
• 76D07

Acknowledgments

We thank the reviewers for valuable comments that have led to some improvements of the present work. The authors are indebted to Prof Mamadou Sango for interesting discussions on Brinkman equations. The work of second author has been sponsored by the University of Pretoria and the National Research Foundation of South Africa.