The linear and non linear Rayleigh-Taylor instability for the quasi isobaric profile

TL;DR

This paper investigates the stability of a quasi-isobaric profile under the Euler equations in a gravity field, addressing challenges due to unbounded profiles and deriving nonlinear stability results from linear analysis.

Contribution

It introduces a novel stability analysis for unbounded quasi-isobaric profiles in Euler equations, linking linear and nonlinear stability in this context.

Findings

Linear stability results for the quasi-isobaric profile

Nonlinear stability deduced from linear analysis

Addressed non-coerciveness due to unbounded profiles

Abstract

We study the stability of the system of the Euler equation in the neighborhood of a stationary profile associated with the quasi isobaric model in a gravity field. This stationary profile is not bounded below, hence the operator is not coercive. We use this linear result to deduce a nonlinear result