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From Navier-Stokes to Measure-Valued Euler-Brinkman Equations: Homogenization in the Inviscid Limit
Abstract
We study the behaviour of the solution to the Navier-Stokes equations with vanishing viscosity and a no-slip condition in a periodically perforated domain. The behaviour depends on the particle size and the viscosity of the fluid. We prove convergence to a measure-valued solution, provided that the local Reynolds number is small, in the subcritical and critical regime. In the first case, the limit solves the Euler equations, whereas in the second case it solves the Euler-Brinkman equations. This extends the results of https://doi.org/10.1088/1361-6544/acfe56 for less regular limit functions. In particular, we also prove existence of measure-valued solutions to the Euler-Brinkman equations, along with weak-strong uniqueness.
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BibTeX
@misc{hofer2026from,
title = {{From Navier-Stokes to Measure-Valued Euler-Brinkman Equations: Homogenization in the Inviscid Limit}},
author = {Richard M. Höfer and Eleni Hübner-Rosenau},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04881},
eprint = {2611.04881},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04881},
}
RIS
TY - UNPB
TI - From Navier-Stokes to Measure-Valued Euler-Brinkman Equations: Homogenization in the Inviscid Limit
AU - Richard M. Höfer
AU - Eleni Hübner-Rosenau
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04881
UR - https://arxiv.org/abs/2611.04881
AB - We study the behaviour of the solution to the Navier-Stokes equations with vanishing viscosity and a no-slip condition in a periodically perforated domain. The behaviour depends on the particle size and the viscosity of the fluid. We prove convergence to a measure-valued solution, provided that the local Reynolds number is small, in the subcritical and critical regime. In the first case, the limit solves the Euler equations, whereas in the second case it solves the Euler-Brinkman equations. This extends the results of https://doi.org/10.1088/1361-6544/acfe56 for less regular limit functions. In particular, we also prove existence of measure-valued solutions to the Euler-Brinkman equations, along with weak-strong uniqueness.
ER -