On the zero capillarity limit for the Euler-Korteweg system
Abstract
We study the Euler-Korteweg equations with a weak capillarity tensor. It formally converges to the Euler equations in the zero capillarity limit. Our aim is two-fold : first we prove rigorously this limit in R d , d 1, and obtain a more precise BKW expansion of the solution, second we initiate the study of the problem on the half space. In this case we obtain a priori estimates for the solutions that degenerate as the capillary coefficient converges to zero, and we explain this degeneracy with the construction of a (formal) BKW expansion that exhibits boundary layers. The results on the full space extend and improve a classical result of Grenier (1998) on the semi-classical limit of nonlinear Schr{\"o}dinger equations. The analysis on the half space is restricted to the case of quantum fluids with irrotational velocity.
Cite
@article{arxiv.2502.10034,
title = {On the zero capillarity limit for the Euler-Korteweg system},
author = {Corentin Audiard and Marc-Antoine Vassenet},
journal= {arXiv preprint arXiv:2502.10034},
year = {2025}
}