Global determination for an inverse problem from the vortex dynamics

TL;DR

This paper demonstrates that it is possible to uniquely reconstruct a real-analytic background potential from vortex dipole dynamics, including boundary measurements, removing previous flatness restrictions.

Contribution

It introduces a method to recover the boundary jet of the potential and removes the flatness assumption in inverse vortex dynamics problems.

Findings

Unique reconstruction of real-analytic potentials from boundary data

Method to recover boundary jet of the potential

Removal of flatness assumption in previous models

Abstract

We consider the problem of reconstructing a background potential from the dynamical behavior of vortex dipole. We prove that under suitable conditions, one can uniquely reconstruct a real-analytic potential by measuring the entrance and exit positions as well as travel times between boundary points. In particular, the work removes the flatness assumption on the potential from the earlier result. A key step of our method is a constructional procedure of recovering the boundary jet of the potential.