Standing Solitary Euler-Korteweg Waves are Unstable

TL;DR

This paper proves that standing solitary waves in the Euler-Korteweg system are inherently unstable, highlighting limitations in their stability properties within fluid dynamics models.

Contribution

It introduces a proof of instability for standing solitary waves in the Euler-Korteweg system, a novel result in the study of such waves.

Findings

Standing solitary waves are unstable in the Euler-Korteweg system.

The instability is rigorously established through mathematical analysis.

This result impacts the understanding of wave stability in fluid models.

Abstract

This short note establishes instability of standing solitary waves in the Euler-Korteweg system.