Continuous data assimilation for the three dimensional primitive equations with magnetic field

In this paper, the problem of continuous data assimilation of three dimensional primitive equations with magnetic field in thin domain is studied. We establish the well-posedness of the assimilation system and prove that the $H^2$-strong solution of the assimilation system converges exponentially to the reference solution in the sense of $L^2$ as $t\to \mathrm{\infty }$. We also study the sensitivity analysis of the assimilation system and prove that a sequence of solutions of the difference quotient equation converge to the unique solution of the formal sensitivity equation.