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The Navier-Stokes system for an incompressible fluid coupled with theequation for a heat transfer is considered in the whole three dimensionalspace. This system is invariant under a suitable scaling. Using theLeray-Schauder theorem and compactness arguments, we construct self-similarsolutions to this system without any smallness assumptions imposed onhomogeneous initial conditions.

Large self-similar solutions to Oberbeck-Boussinesq system with newtonian gravitational field