Global well-posedness and large-time behavior for the 3D full compressible Navier-Stokes equations with density-dependent viscosity and vacuum

• Published in: Journal of Differential Equations Vol. 426; pp. 466 - 494
• Main Authors: Shen, Linxuan, Xu, Hao, Zhang, Jianwen
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 05.05.2025
• Subjects: Compressible Navier-Stokes equations; Density-dependent viscosity; Global strong solutions; Initial-boundary value problem; Vacuum; Vacuum; 35B45; Density-dependent viscosity; Initial-boundary value problem; 35B40; Global strong solutions; 76N10; Compressible Navier-Stokes equations
• ISSN: 0022-0396
• DOI: 10.1016/j.jde.2025.01.072

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.