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In this paper, we investigate the uniform regularity for the isentropiccompressible Navier-Stokes system with general Navier-slip boundary conditions(1.6) and the inviscid limit to the compressible Euler system. It is shown thatthere exists a unique strong solution of the compressible Navier-Stokesequations with general Navier-slip boundary conditions in an interval of timewhich is uniform in the vanishing viscosity limit. The solution is uniformlybounded in a conormal Sobolev space and is uniform bounded in $W^{1,\infty}$.It is also shown that the boundary layer for the density is weaker than the onefor the velocity field. In particular, it is proved that the velocity will beuniform bounded in $L^\infty(0,T;H^2)$ when the boundary is flat and theNavier-Stokes system is supplemented with the special boundary condition(1.21). Based on such uniform estimates, we prove the convergence of theviscous solutions to the inviscid ones in $L^\infty(0,T;L^2)$,$L^\infty(0,T;H^1)$ and $L^\infty([0,T]\times\Omega)$ with a rate ofconvergence.

Uniform regularity and vanishing viscosity limit for the compressible  Navier-Stokes with general Navier-slip boundary conditions in 3-dimensional  domains