Global well-posedness and large-time behavior for the 3D full compressible Navier-Stokes equations with density-dependent viscosity and vacuum - Shen, Linxuan; Xu, Hao; Zhang, Jianwen (Journal of Differential Equations, 2025)
This paper is concerned with an initial-boundary value problem of full compressible Navier-Stokes equations with density-dependent viscosity on 3D bounded domains subject to Dirichlet boundary conditions. The global well-posedness of strong solutions with vacuum is established, provided the initial total energy is suitably small. As by-products, the exponential decay estimates of the solutions are also obtained. There is no smallness condition on the density and its gradient.