Global strong solutions to the 3D full compressible Navier-Stokes equations with density-temperature-dependent viscosities in bounded domains

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 theta admit the Dirichlet boundary condition, the strong solutions exist globally in time provided that parallel to del u(0)parallel to(2)(L2) + parallel to del theta(0)parallel to(2)(L2) 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. (C) 2019 Elsevier Inc. All rights reserved.