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.