Résumé en anglais

In this paper we are interested in the barotropic compressible Navier-Stokes system endowed with a non-local capillarity tensor depending on a small parameter Epsilon such that it heuristically tends to the local Korteweg system. After giving some physical motivations related to the theory of non-classical shocks (see [28]) we prove global well-posedness (in the whole space Rd w ith d ≥ 2) for the non-local model and we also prove the convergence, as Epsilon goes to zero, to the solution of the local Korteweg system.