Global identifiability of low regularity fluid parameters in acoustic tomography of moving fluid

TL;DR

This paper demonstrates that boundary measurements can uniquely determine low regularity fluid parameters in acoustic tomography, even allowing for discontinuities, thus advancing inverse boundary problem theory for moving fluids.

Contribution

It establishes unique identifiability of low regularity fluid parameters in acoustic tomography, extending previous results to include discontinuous parameters and weaker regularity assumptions.

Findings

Boundary measurements determine low regularity fluid parameters.

The results include cases with discontinuous fluid parameters.

The work sharpens regularity assumptions compared to prior studies.

Abstract

We are concerned with inverse boundary problems for first order perturbations of the Laplacian, which arise as model operators in the acoustic tomography of a moving fluid. We show that the knowledge of the Dirichlet--to--Neumann map on the boundary of a bounded domain in $\mathbb{R}^n$, $n\ge 3$, determines the first order perturbation of low regularity up to a natural gauge transformation, which sometimes is trivial. As an application, we recover the fluid parameters of low regularity from boundary measurements, sharpening the regularity assumptions in the recent results of [1] and [3]. In particular, we allow some fluid parameters to be discontinuous.