Global regularity to the Cauchy problem of the 3D heat conducting incompressible Navier–Stokes equations

This paper concerns the global regularity to the Cauchy problem of the 3D heat conducting incompressible Navier–Stokes equations with density-temperature-dependent viscosity and vacuum. Through the t-weighted a priori estimates, we establish the global existence and decay of strong solutions provided the initial energy is suitably small. It should be noted that the absolute temperature can be large initially.