Almost periodic solutions of Boussinesq systems in the whole space

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In this paper, we investigate the well-posedness and polynomial stability of almost periodic mild solutions for Boussinesq systems on the whole space R n (for dimension n ⩾ 3 ) and whole line time-axis R t in framework of weak-Morrey spaces. By using linear and bilinear estimates on Morrey–Lorentz spaces, we prove the existence of bounded mild solutions for the corresponding linear systems on the whole line time-axis R t . Then we obtain the well-posedness of almost periodic solutions to the linear systems. By using fixed point arguments, we establish the well-posedness and polynomial stability of such solutions for Boussinesq systems.