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We study the behavior at infinity, with respect to the space variable, ofsolutions to the magnetohydrodynamics equations in ${\bf R}^d$. We prove thatif the initial magnetic field decays sufficiently fast, then the plasma flowbehaves as a solution of the free nonstationnary Navier--Stokes equations when$|x|\to +\infty$, and that the magnetic field will govern the decay of theplasma, if it is poorly localized at the beginning of the evolution. Our maintools are boundedness criteria for convolution operators in weighted spaces.

On the localization of the magnetic and the velocity fields in the equations of magnetohydrodynamics