Global existence and large time behavior of strong solutions for 3D nonhomogeneous heat conducting Navier–Stokes equations

Abstract

We are concerned with an initial boundary value problem of nonhomogeneous heat conducting Navier–Stokes equations on a bounded simply connected smooth domain Ω⊆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 ‖ρ0u0‖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.