On the well-posedness of the damped time-harmonic Galbrun equation and the equations of stellar oscillations

TL;DR

This paper proves the well-posedness of the damped time-harmonic Galbrun equation, a key model for sound propagation in steady flows and stellar oscillations, under mild conditions using a generalized Helmholtz decomposition.

Contribution

It establishes the existence, uniqueness, and stability of solutions for the damped Galbrun equation with subsonic flows, advancing the mathematical understanding of stellar oscillation models.

Findings

Proved well-posedness of the damped Galbrun equation.

Applied a generalized Helmholtz decomposition in the analysis.

Results hold under mild subsonic flow conditions.

Abstract

We study the time-harmonic Galbrun equation describing the propagation of sound in the presence of a steady background flow. With additional rotational and gravitational terms these equations are also fundamental in helio- and asteroseismology as a model for stellar oscillations. For a simple damping model we prove well-posedness of these equations, i.e. uniqueness, existence, and stability of solutions under mild conditions on the parameters (essentially subsonic flows). The main tool of our analysis is a generalized Helmholtz decomposition.