We consider the convection problem of a fluid with viscosity depending on tempera-ture in either a bounded or an exterior domain Ω⊂ RN,N =2,3. It is assumed that the temperature is transported without thermal conductance (dissipation) by the velocity field which is described by the Navier-Stokes flow. This model is commonly called the Boussinesq system with partial viscosity. In this paper we prove the existence and uniqueness of strong solutions for the Boussinesq system with partial viscosity with initial data in W2-2/p,p(Ω)×W1,q(Ω). For a bounded domain Ω, we also analyze the inviscid limit problem when the conductivity in the fully viscous Boussinesq system goes to zero. © 2013 International Press.112421439de Almeida, M., Ferreira, L.C.F., On the well posedness and large-time behavior for Boussi-nesq equations in Morrey spaces (2011) Diff. 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