Inverse coefficient problem for a magnetohydrodynamics system by Carleman estimates

In this article, we consider a magnetohydrodynamics system for incompressible flow in a three-dimensional bounded domain. Firstly, we state the stability results for our inverse coefficient problem. Secondly, we establish and prove two Carleman type inequalities both for the solutions and for the unknown coefficients. Finally, we complete the proofs of the stability results in terms of the above Carleman estimates.

Automated summary

This article examines a magnetohydrodynamics system for incompressible flow in a three-dimensional bounded domain, presenting stability results for the inverse coefficient problem and Carleman type inequalities for solutions and unknown coefficients. The proofs of the stability results are completed based on the Carleman estimates provided.