Boundary observability for gas giant metrics

TL;DR

This paper investigates the observability of acoustic waves on gas giant manifolds with singular boundary metrics, establishing an inequality using boundary measurements and advanced analytical techniques.

Contribution

It introduces a novel observability inequality for gas giant metrics, reducing the problem to a separable case and employing frequency analysis and Ingham inequality.

Findings

Established an observability inequality for gas giant manifolds.

Reduced general observability to a separable case via perturbation.

Applied frequency analysis and Ingham inequality to prove observability.

Abstract

We study the observability of waves on gas giant manifolds which are a class of Riemannian manifolds whose metrics are singular at the boundary. Such manifolds arise naturally in modeling of acoustic wave propagation in gas giant planets.We establish an observability inequality using full boundary measurements given by a Neumann-type trace that is natural in the gas giant setting. The proof proceeds in two steps. First, observability for a general gas giant metric is reduced to the so-called separable case via a perturbation argument. In the separable case, we employ a uniform-in-tangential-frequency analysis combined with an Ingham inequality to prove observability.