On the limit of large surface tension for a fluid motion with free boundary

TL;DR

This paper investigates the behavior of free boundary Euler equations in two dimensions, demonstrating that solutions converge to fixed domain solutions as surface tension becomes very large, assuming boundary regularity.

Contribution

It establishes the limiting behavior of free boundary fluid motions with large surface tension, connecting free boundary solutions to fixed domain Euler solutions.

Findings

Solutions converge to fixed domain Euler solutions as surface tension increases.

Boundary regularity is crucial for the convergence result.

Provides a rigorous mathematical link between free boundary and fixed boundary flows.

Abstract

We study the free boundary Euler equations in two spatial dimensions. We prove that if the boundary is sufficiently regular, then solutions of the free boundary fluid motion converge to solutions of the Euler equations in a fixed domain when the coefficient of surface tension tends to infinity.