Partial regularity for an elliptic-parabolic system modeling miscible fluid flows in porous media

TL;DR

This paper investigates the existence and partial regularity of weak solutions to a singular elliptic-parabolic system modeling the displacement of one incompressible fluid by another in porous media, using advanced inequality techniques.

Contribution

It provides new partial regularity results for a complex nonlinear system modeling fluid flow in porous media, extending previous mathematical understanding.

Findings

Established existence of weak solutions.

Proved partial regularity using Fefferman-Stein inequality.

Addressed singular and quadratic nonlinearities in the system.

Abstract

In this paper we study the existence and partial regularity of weak solutions to an elliptic-parabolic system that models the single-phase miscible displacement of one incompressible fluid by another in a porous media. The system is singular and involves quadratic nonlinearity. A partial regularity result is obtained via the Fefferman-Stein inequality.