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. We consider the convection problem of a fluid with viscosity depending on temperature in either a bounded or an exterior domain Ω⊂R ,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

Strong solutions and inviscid limit for Boussinesq system with partial viscosity