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

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Date
2011
Link to item file
http://arxiv.org/abs/1101.2398v1
Dewey
Analyse
Sujet
Navier–Stokes system; Korteweg system
Journal issue
Indiana University Mathematics Journal
Volume
60
Number
6
Publication date
2011
Article pages
2021-2060
Publisher
Indiana University
DOI
http://dx.doi.org/10.1512/iumj.2011.60.4600
URI
https://basepub.dauphine.fr/handle/123456789/7229
Collections
  • CEREMADE : Publications
Metadata
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Author
Haspot, Boris
Charve, Frédéric
Type
Article accepté pour publication ou publié
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.

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