Abstract: By using the harmonic analysis method and Lagrangian method, we studied the Cauchy problem for the multi-dimensional inhomogeneous incompressible heat-conducting equations and  proved the global well-posedness of strong solutions for the system under small initial data conditions in the critical Besov spaces.

Key words:  , inhomogeneous incompressible heat-conducting equation, critical Besov space, Lagrangian coordinate, well-posedness