On the Existence of Strong Solutions to the Cahn-Hilliard-Darcy system with mass source

TL;DR

This paper proves the existence and uniqueness of strong solutions for a Cahn-Hilliard-Darcy system with mass source, modeling binary fluid flow and tumor growth in Hele-Shaw cells, in two and three dimensions.

Contribution

It establishes the first rigorous results on global strong solutions for the CHD system with mass source, including in physically relevant three-dimensional cases.

Findings

Global existence and uniqueness of strong solutions in 2D.

Local existence of solutions in 3D.

Application to tumor growth modeling.

Abstract

We study a diffuse interface model describing the evolution of the flow of a binary fluid in a Hele-Shaw cell. The model consists of a Cahn-Hilliard-Darcy (CHD) type system with transport and mass source. A relevant physical application is related to tumor growth dynamics, which in particular justifies the occurrence of a mass inflow. We study the initial-boundary value problem for this model and prove global existence and uniqueness of strong solutions in two space dimensions as well as local existence in three space dimensions.