Convergence of capillary fluid models: from the non-local to the local Korteweg model
Résumé
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 $\ee$ such that it heuristically tends to the local Korteweg system. After giving some explanations about the capillarity (physical justification and purpose, motivations related to the theory of non-classical shocks (see \cite{Lefloch})), we prove global well-posedness (in the whole space $\R^d$ with $d\geq 2$) for the non-local model, as well as the convergence, as $\ee$ goes to zero, to the solution of the local Korteweg system.
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