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arXiv · 1410.8777

Highly rotating viscous compressible fluids in presence of capillarity effects

Francesco Fanelli
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Abstract

In this paper we study a singular limit problem for a Navier-Stokes-Korteweg system with Coriolis force, in the domain $\R^2\times\,]0,1[\,$ and for general ill-prepared initial data. Taking the Mach and the Rossby numbers to be proportional to a small parameter $\veps$ going to $0$, we perform the incompressible and high rotation limits simultaneously. Moreover, we consider both the constant capillarity and vanishing capillarity regimes. In this last case, the limit problem is identified as a $2$-D incompressible Navier-Stokes equation in the variables orthogonal to the rotation axis. If the capillarity is constant, instead, the limit equation slightly changes, keeping however a similar structure. Various rates at which the capillarity coefficient can vanish are also considered: in most cases this will produce an anisotropic scaling in the system, for which a different analysis is needed. The proof of the results is based on suitable applications of the RAGE theorem.

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Francesco Fanelli. 2017-08-16. Highly rotating viscous compressible fluids in presence of capillarity effects. https://arxiv.org/abs/1410.8777

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