Global strong solutions for 3D viscous incompressible heat conducting Navier‐Stokes flows with the general external force

In this paper, we consider the initial boundary value problem for the nonhomogeneous heat–conducting fluids with non‐negative density and the general external force. We prove that there exists a unique global strong solution to the 3D viscous nonhomogeneous heat–conducting Navier‐Stokes flows if μ − 4ρ ¯ 3 ( ‖ ρ u 0‖L 22 + ‖ f ‖L t 2L x 2) ( ‖ ∇ u 0‖L 22 + 5 2μ − 1ρ ¯ ‖ f ‖L t 2L x 2) is suitably small.