A singular limit problem for rotating capillary fluids with variable rotation axis

TL;DR

This paper investigates the combined effects of fast rotation and capillarity in fluid dynamics with variable rotation axes, proving convergence to a parabolic equation using advanced compactness techniques.

Contribution

It introduces a novel analysis of the singular limit for Navier-Stokes-Korteweg fluids with variable rotation axis, extending previous models to more general and realistic scenarios.

Findings

Convergence to a linear parabolic-type equation with variable coefficients.

Established minimal regularity conditions for the rotation axis variations.

Applied compensated compactness to handle the singular perturbation.

Abstract

In the present paper we study a singular perturbation problem for a Navier-Stokes-Korteweg model with Coriolis force. Namely, we perform the incompressible and fast rotation asymptotics simultaneously, while we keep the capillarity coefficient constant in order to capture surface tension effects in the limit. We consider here the case of variable rotation axis: we prove the convergence to a linear parabolic-type equation with variable coefficients. The proof of the result relies on compensated compactness arguments. Besides, we look for minimal regularity assumptions on the variations of the axis.