Duchon-Robert solutions for the Rayleigh-Taylor and Muskat problems

TL;DR

This paper extends Duchon and Robert's work to construct analytic solutions for the Euler equations with fluid interfaces and demonstrates that their estimates provide global solutions to the Muskat problem with small initial data.

Contribution

It introduces new analytic solutions for fluid interface problems and applies Duchon and Robert's estimates to establish global solutions for the Muskat problem.

Findings

Constructed analytic solutions for Euler equations with fluid interfaces.

Established global solutions for the Muskat problem with small initial data.

Extended Duchon and Robert's previous work to new fluid dynamics problems.

Abstract

We construct analytic solutions to the Euler equations with an interface between two fluids, extending work of Duchon and Robert. We also show that the estimates of Duchon and Robert yield global analytic solutions to the Muskat problem with small initial data.