An inverse problem for compressible Euler's equations

TL;DR

This paper investigates an inverse problem for compressible Euler's equations, demonstrating that active measurements near a particle trajectory can determine the background flow in certain regions, assuming nonzero vorticity.

Contribution

It introduces a method to recover background flow from active measurements in compressible Euler's equations with nonzero vorticity.

Findings

Active measurements near a particle trajectory can determine the background flow.

The method applies in regions where pressure waves propagate from and return to the trajectory.

Assumption of nonzero vorticity is crucial for the analysis.

Abstract

We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can propagate from and return to the particle trajectory, under the additional assumption that the flow has nonzero vorticity.