  We prove the convergence of the vanishing viscosity limit of the
one-dimensional, isentropic, compressible Navier-Stokes equations to the
isentropic Euler equations in the case of a general pressure law. Our strategy
relies on the construction of fundamental solutions to the entropy equation
that remain controlled for unbounded densities, and employs an improved
reduction framework to show that measure-valued solutions constrained by the
Tartar commutation relation (but with possibly unbounded support) reduce to a
Dirac mass. As the Navier-Stokes equations do not admit an invariant region, we
work in the finite-energy setting, where a detailed understanding of the high
density regime is crucial.
