Large friction limit of compressible Navier--Stokes equations with Navier boundary conditions in a half-space

We study the large-friction limit for the three-dimensional barotropic compressible Navier-Stokes equations in a half-space. The velocity satisfies a Navier boundary condition with friction coefficient $\alpha >0$, while the limiting problem satisfies the no-slip boundary condition. We establish estimates for local-in-time smooth solutions that are uniform in $\alpha$ and prove strong convergence of the density and velocity as $\alpha \to \mathrm{\infty }$. For weak solutions, we use the Lagrangian flow maps associated with the two velocities to compare the densities and construct suitable transported test functions. This yields weak convergence to the no-slip solution. Our results provide a compressible counterpart of the large-friction limit for incompressible flows.