Convergence of capillary fluid models: from the non-local to the local Korteweg model Frédéric CharveBoris Haspot 35Q30 35Q35 76N10PDEKortewegbesov spacescapillarityasymptotics 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 formally 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 [P.G. LeFloch, \textit{Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves}, Lectures in Mathematics ETH Z\"urich, Birkh\"auser Verlag, Basel, 2002])), we prove global well-posedness (in the whole space $\mathbb{R}^d$ with $d \geq 2$) for the non-local model, as well as the convergence, as $\epsilon$ goes to zero, to the solution of the local Korteweg system. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4600 10.1512/iumj.2011.60.4600 en Indiana Univ. Math. J. 60 (2011) 2021 - 2060 state-of-the-art mathematics http://iumj.org/access/