Singular limits for non-isentropic compressible rotating fluids

TL;DR

This paper investigates the singular limits of non-isentropic compressible rotating fluids with capillary effects, deriving convergence results and dispersion estimates for Navier-Stokes-Korteweg equations under various regimes.

Contribution

It introduces new convergence results for Navier-Stokes-Korteweg equations with capillary effects in rotating fluids, including low Mach and Rossby number limits, and connects three-dimensional models to two-dimensional incompressible Euler equations.

Findings

Derived dispersion estimates for acoustic waves using Rage's theorem.

Established convergence of Navier-Stokes-Korteweg equations to incompressible Euler equations.

Analyzed effects of capillarity in singular limits of rotating fluid models.

Abstract

In this article, we study the singular limit of non-isentropic compressible rotating fluids. We incorporate the capillary effect into both the $\alpha=1$ and $\alpha=0$ cases, and investigate the Navier-Stokes-Korteweg equations involving the terms of low Mach number, low Rossby number and high Reynolds number. When $\alpha=1$, the dispersion estimate of the acoustic wave equation is derived by Rage's theorem. When $\alpha=0$, we obtain the convergence results by error estimate. Moreover, we obtain that the three dimensions compressible Navier-Stokes-Korteweg equations converge to the two dimensions incompressible Euler equations.