On the Well-Posedness of Generalized Darcy Forchheimer Equation

TL;DR

This paper proves the existence, uniqueness, and stability of solutions for the generalized Darcy-Forchheimer equation under certain conditions, advancing the mathematical understanding of this fluid flow model.

Contribution

It establishes well-posedness results for the generalized Darcy-Forchheimer equation with minimal regularity assumptions, filling a gap in the mathematical theory.

Findings

Existence of solutions under compatibility conditions

Uniqueness of solutions for the model

Stability of solutions with respect to data

Abstract

Under necessary compatibility condition, and some mild regularity assumptions on the interior and the boundary data, we prove the existence, uniqueness, and stability of the solution of generalized Dary-Forchheimer model.