Virial Theorem and Its Applications in Instability of Two-Phase Water-Wave

TL;DR

This paper derives a virial theorem for two-layer water-wave systems and proves the polynomial growth of interface slope and curvature, demonstrating Rayleigh-Taylor instability under broad initial conditions.

Contribution

It establishes a virial theorem and proves polynomial growth of interface features, advancing understanding of instability in two-phase water-wave systems.

Findings

Polynomial growth of interface slope and curvature

Rayleigh-Taylor instability demonstrated for broad initial data

Virial theorem established for nonlinear water-wave dynamics

Abstract

In this paper, we analyze the dynamics of two layers of immiscible, inviscid, incompressible, and irrotational fluids through a full nonlinear system. Our goal is to establish a virial theorem and prove the polynomial growth of slope and curvature of the interface over time when the fluid below is no denser than the one above. These phenomena, known as Rayleigh-Taylor instability, will be proved for a broad class of regular initial data, including the case of 2D overlapping interface.