An asymptotic limit of a Navier-Stokes system with capillary effects
Analysis of PDEs
2015-06-12 v1
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.
Keywords
Cite
@article{arxiv.1302.1299,
title = {An asymptotic limit of a Navier-Stokes system with capillary effects},
author = {A. Jüngel and C. -K. Lin and K. -C. Wu},
journal= {arXiv preprint arXiv:1302.1299},
year = {2015}
}