The free boundary Euler equations with large surface tension

TL;DR

This paper investigates the well-posedness of free boundary Euler equations with surface tension in 3D and demonstrates convergence to fixed boundary solutions as surface tension increases.

Contribution

It establishes well-posedness for the equations with positive surface tension and proves convergence to fixed boundary solutions as surface tension tends to infinity.

Findings

Equations are well-posed with positive surface tension

Solutions converge to fixed boundary solutions as surface tension increases

Provides mathematical foundation for boundary behavior in fluid dynamics

Abstract

We study the free boundary Euler equations with surface tension in three spatial dimensions, showing that the equations are well-posed if the coefficient of surface tension is positive. Then we prove that under natural assumptions, the solutions of the free boundary motion converge to solutions of the Euler equations in a domain with fixed boundary when the coefficient of surface tension tends to infinity.