An Asymptotic Limit of a Navier-Stokes System with Capillary Effects

Ansgar Jüngel*, Chi Kun Lin, Kung Chien Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


A combined incompressible and vanishing capillarity limit in the barotropic compressible Navier-Stokes equations for smooth solutions is proved. The equations are considered on the two-dimensional torus with well prepared initial data. The momentum equation contains a rotational term originating from a Coriolis force, a general Korteweg-type tensor modeling capillary effects, and a density-dependent viscosity. The limiting model is the viscous quasi-geostrophic equation for the "rotated" velocity potential. The proof of the singular limit is based on the modulated energy method with a careful choice of the correction terms.

Original languageEnglish
Pages (from-to)725-744
Number of pages20
JournalCommunications in Mathematical Physics
Issue number2
Publication statusPublished - Jul 2014
Externally publishedYes


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