Weak solutions of the convective Cahn-Hilliard equation with degenerate mobility

TL;DR

This paper proves the existence of weak solutions for a convective Cahn-Hilliard equation with degenerate mobility by analyzing regularized problems and their limits.

Contribution

It introduces a new framework for weak solutions and demonstrates their existence for a complex convective Cahn-Hilliard model with degeneracy.

Findings

Existence of weak solutions established

Regularized problems approach used for proof

Framework applicable to similar degenerate PDEs

Abstract

In this paper, the existence of weak solutions of a convective Cahn-Hilliard equation with degenerate mobility is studied. We first define a notion of weak solutions and establish a regularized problems. The existence of such solutions is obtained by considered the limits of the regularized problems.