Inverse coefficients problem for a magnetohydrodynamics system

TL;DR

This paper investigates an inverse coefficients problem for a 3D magnetohydrodynamics system, establishing stability results and Carleman estimates to advance understanding of the system's inverse properties.

Contribution

It introduces new Carleman estimates and stability results specifically for the inverse coefficients problem in magnetohydrodynamics systems.

Findings

Established stability results for the inverse coefficients problem.

Proved two new Carleman estimates for the direct and inverse problems.

Completed the proof of stability using these Carleman estimates.

Abstract

In this article, we consider a magnetohydrodynamics system for incompressible flow in a three-dimensional bounded domain. Firstly, we give the stability results for our inverse coefficients problem. Secondly, we establish and prove two Carleman estimates for both direct problem and inverse problem. Finally, we complete the proof of stability result in terms of the above Carleman estimates.