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arXiv · 1302.1299

An asymptotic limit of a Navier-Stokes system with capillary effects

A. Jüngel·C. -K. Lin·K. -C. Wu
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Abstract

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.

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A. Jüngel, C. -K. Lin, K. -C. Wu. 2013-02-06. An asymptotic limit of a Navier-Stokes system with capillary effects. https://doi.org/10.1007/s00220-014-1961-9

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