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We consider the initial boundary problem of 2D non-homogeneous incompressibleheat conducting Navier-Stokes equations with vacuum, where the viscosity andheat conductivity depend on temperature in a power law of Chapman-Enskog. Wederive the global existence of strong solution to the initial-boundary valueproblem, which is not trivial, especially for the nonisentropic system withvacuum. Significantly, our existence result holds for the cases that theviscosity and heat conductivity depend on $\theta$ with possibly differentpower laws (i.e., $\mu=\theta^{\alpha}, \kappa=\theta^{\beta}$ with constants $\alpha,\beta\geq0$) with smallness assumptions only on $\alpha$ and the measureof initial vacuum domain. In particular, the initial data can be arbitrarilylarge. Moreover, it is obtained that both velocity and temperature decayexponentially as time tends to infinity.

Global well-posedness for the 2D incompressible heat conducting Navier-Stokes equations with temperature-dependent coefficients and vacuum