Global existence and large time behavior of strong solutions for 3D nonhomogeneous heat conducting Navier-Stokes equations (October, 2020)

We are concerned with an initial boundary value problem of nonhomogeneous heat conducting Navier-Stokes equations on a bounded simply connected smooth domain omega subset of R3, with the Navier-slip boundary condition for velocity and Neumann boundary condition for temperature. We prove that there exists a unique global strong solution, provided that ||rho 0u0||L22||curlu0||L22 is suitably small. Moreover, we also obtain the large time decay rates of the solution. Our result improves previous works on this topic.