Large time behavior of solutions to a Stokes-Magneto equations in three dimensions

This paper is devoted to the large time decay of solutions of a three-dimensional Stokes-Magneto equations. It is shown that, when initial data belong to $$L^2$$ , weak solutions of the equations decay to zero in $$L^{3/2,\infty }\times L^2$$ without a uniform rate, and this decay estimate is optimal. Furthermore, the optimal temporal decay estimates for weak solutions are established when initial data belongs to $$L^1\cap L^2$$ .