Inviscid incompressible limit for capillary fluids with density dependent viscosity

2025/07/01 by Matteo Caggio, Donatella Donatelli, Caggio, Matteo +3 · 1 citation
Earth and Planetary Sciences · Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing

paper · pdf · doi:10.48550/arxiv.2507.00621

openalex publication_date 2025/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The asymptotic limit of the 2D and 3D Navier-Stokes-Korteweg system for barotropic capillary fluids with density dependent viscosities in the low Mach number and vanishing viscosity regime is established. In the relative energy framework, we prove the convergence of weak solutions of the Navier-Stokes-Korteweg system to the strong solution of the incompressible Euler system. The convergence is obtained through the use of suitable dispersive estimates for an acoustic system altered by the presence of the Korteweg tensor.

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