Abstract
In this paper, we study the global strong solutions to the three-dimensional (3D) heat-conducting incompressible Navier–Stokes equations with density-temperature-dependent viscosity and heat-conducting coefficients in . By using the t-weighted a priori estimates, we prove the global existence and exponential decay-in-time rates of strong solutions to the Cauchy problem when the -norm of the initial density is suitably small. It should be noted that the velocity and absolute temperature can be large initially, and the initial density contains vacuum case.
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