Abstract
We study the inverse problem for non-stationary system of magnetic hydrodynamics in which it is required to determine the velocity of the fluid $\vec{v}(x,t)$ , the magnetic tension $\vec{H}(x,t)$ , the pressure gradient $\nabla p(x,t)$ , but also the external forces $\vec{f}(x)$ and the current $\operatorname{rot}\vec{j}(x)$ . In this case, to the conditions constituting the direct problem are added additional conditions. The trace speed, the magnetic tension, and the pressure gradient in the final moment, time $t=T$ , are taken as additional information. The strong generalized solvability of the inverse problem in the two-dimensional case is proved.