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.

中文翻译：

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3D 非均匀导热 Navier-Stokes 方程强解的全局存在性和大时间行为

我们关注有界单连通光滑域Ω⊆R3上的非齐次热传导纳维-斯托克斯方程的初始边界值问题，速度是纳维滑移边界条件，温度是诺依曼边界条件。我们证明存在唯一的全局强解，条件是‖ρ0u0‖L22‖curlu0‖L22 适当小。此外，我们还获得了解的大时间衰减率。我们的结果改进了以前关于这个主题的工作。