Global well-posedness for the compressible Navier--Stokes equations in 3D bounded domains under a new smallness condition

We investigate the three-dimensional barotropic compressible Navier–Stokes equations involving vacuum in a bounded domain with Navier-slip boundary conditions. It is shown that such a model admits a unique global strong solution provided the gradient of the initial velocity and the initial pressure deviation are suitably small in $L^2$. In particular, $\mathit{\text{the}}\mathit{\text{smallness}}\mathit{\text{threshold}}\mathit{\text{depends}}\mathit{\text{only}}\mathit{\text{on}}\mathit{\text{the}}\mathit{\text{known}}\mathit{\text{parameters}}\mathit{\text{and}}\mathit{\text{the}}\mathit{\text{prescribed}}\mathit{\text{density}}\mathit{\text{bounds.}}$ Our result provides a new analytical framework for the global well-posedness theory of the compressible Navier–Stokes equations.