Carleman estimates for a magnetohydrodynamics system and application to inverse source problems

Abstract

In this article, we consider a linearized magnetohydrodynamics system for incompressible flow in a three-dimensional bounded domain. We first prove two kinds of Carleman estimates. This is done by combining the Carleman estimates for the parabolic and the elliptic equations. Then we apply the Carleman estimates to prove Hölder type stability results for some inverse source problems.