On a Lagrangian method for the convergence from a non-local to a local Korteweg capillary fluid model
Charve, Frédéric; Haspot, Boris (2013), On a Lagrangian method for the convergence from a non-local to a local Korteweg capillary fluid model, Journal of Functional Analysis, 265, 7, p. 1264-1323. http://dx.doi.org/10.1016/j.jfa.2013.05.042
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00787265
Journal nameJournal of Functional Analysis
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Abstract (EN)In the present article we are interested in further investigations for the barotropic compressible Navier-Stokes system endowed with a non-local capillarity we studied in . Thanks to an accurate study of the associated linear system using a Lagrangian change of coordinates, we provide more precise energy estimates in terms of hybrid Besov spaces naturally depending on a threshold frequency ( which is determined in function of the physical parameter) distinguishing the low and the high regimes. It allows us in particular to prove the convergence of the solutions from the non-local to the local Korteweg system. Another mathematical interest of this article is the study of the effect of the Lagrangian change on the non-local capillary term.
Subjects / KeywordsBesov spaces; Capillary models; Lagrangian flow; Compressible Navier–Stokes in critical spaces
Showing items related by title and author.
Existence of global strong solution and vanishing capillarity-viscosity limit in one dimension for the Korteweg system Haspot, Boris; Charve, Frédéric (2013) Article accepté pour publication ou publié