Orthogonality conditions and asymptotic stability in the Stefan problem with surface tension

TL;DR

This paper proves the nonlinear asymptotic stability of steady spherical solutions in the two-phase Stefan problem with surface tension, using orthogonality conditions and a high-order energy method.

Contribution

It introduces a novel approach combining orthogonality conditions with a high-order energy method to establish stability in the Stefan problem.

Findings

Steady spheres are proven to be asymptotically stable.

Orthogonality conditions are effective in analyzing stability.

The method can be applied to similar free boundary problems.

Abstract

We prove nonlinear asymptotic stability of steady spheres in the two-phase Stefan problem with surface tension. Our method relies on the introduction of appropriate orthogonality conditions in conjunction with a high-order energy method.