Abstract We consider the three–dimensional full compressible Navier–Stokes system with density–temperature–dependent viscosities in smooth bounded domains. For the case when the velocity u and absolute temperature θ admit the Dirichlet boundary condition, the strong solutions exist globally in time provided that ‖ ∇ u 0 ‖ L 2 2 + ‖ ∇ θ 0 ‖ L 2 2 is suitably small. Through some time–weighted a priori estimates, the main difficulties caused by the density–temperature–dependent viscosities and the bounded domain are overcome. Moreover, the time–uniform upper bounds for the L p –norm of the gradient of the density are obtained, which is of independent interest for compressible fluids when initial vacuum is allowed.

中文翻译：

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3D 完全可压缩 Navier-Stokes 方程的全局强解在有界域中具有密度-温度相关的粘度

摘要 我们考虑在光滑有界域中具有密度-温度相关粘度的三维完全可压缩 Navier-Stokes 系统。对于速度 u 和绝对温度 θ 满足狄利克雷边界条件的情况，只要 ‖ ∇ u 0 ‖ L 2 2 + ‖ ∇ θ 0 ‖ L 2 2 适当小，强解在时间上全局存在。通过一些时间加权的先验估计，克服了由密度-温度相关的粘度和有界域引起的主要困难。此外，获得了密度梯度的 L p 范数的时间均匀上限，当允许初始真空时，这对于可压缩流体是独立的。