# Growth in the Muskat problem

## TL;DR

This paper reviews recent advances in the Muskat problem, a model for multiphase flow in porous media, and introduces a new regularity criterion based on initial data norms in critical function spaces.

## Contribution

It provides a comprehensive review of recent results and establishes a novel regularity criterion in critical spaces for the Muskat problem.

## Key findings

- New regularity criterion in critical spaces
- Enhanced understanding of initial data impact
- Summary of recent progress in the field

## Abstract

We review some recent results on the Muskat problem modelling multiphase flow in porous media. Furthermore, we prove a new regularity criterion in terms of some norms of the initial data in critical spaces ($\dot{W}^{1,\infty}$ and $\dot{H}^{3/2}$).