On existence and uniqueness of mild solutions for Boussinesq systems in Besov–Morrey-type spaces

In this paper, we investigate the global existence and unconditional uniqueness of mild solutions for the incompressible Boussinesq systems in Besov-weak-Morrey spaces on Rn with n⩾3. Our approach begins by establishing linear and bilinear estimates for operators associated with linear systems. These estimates are then utilized to prove the global well-posedness of linear systems in Besov-weak-Morrey spaces. Building on these results and applying fixed point arguments, we demonstrate the well-posedness of semilinear systems. Finally, we establish the uniqueness of mild solutions for the Boussinesq systems without imposing any smallness conditions on the initial data.