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

Haspot, Boris; Charve, Frédéric

Haspot, Boris; Charve, Frédéric (2011), Convergence of capillary fluid models: from the non-local to the local Korteweg model, Indiana University Mathematics Journal, 60, 6, p. 2021-2060. http://dx.doi.org/10.1512/iumj.2011.60.4600

Type

Article accepté pour publication ou publié

External document link

http://arxiv.org/abs/1101.2398v1

Date

2011

Journal name

Indiana University Mathematics Journal

Volume

Number

Publisher

Indiana University

Pages

2021-2060

Abstract (EN)

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.

Subjects / Keywords

Navier–Stokes system; Korteweg system