Convergence of capillary fluid models: from the non-local to the local Korteweg model

Details Convergence of capillary fluid models: from the non-local to the local Korteweg model Convergence of capillary fluid models: from the non-local to the local Korteweg model

2011-01-12

arxiv.org/abs/1101.2398v1

Mathematics

Analysis of PDEs

Scientific paper

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 $R^d$ with $d\geq 2$) for the non-local model and we also prove the convergence, as $\epsilon$ goes to zero, to the solution of the local Korteweg system.

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