Time-periodic forcing and asymptotic stability for the Navier Stokes   Maxwell equations
  For the 3D Navier-Stokes-Maxwell problem on the whole space and in the presence of external time-periodic forces, first we study the existence of time-periodic small solutions, and then we prove their asymptotic stability. We use new type of spaces to account for averaged decay in time. 
Slim Ibrahim, Pierre-Gilles Lemarie and Nader Masmoudi
math.AP