arXiv subjects

Eleni Hübner-Rosenau

Publications and source records attributed to Eleni Hübner-Rosenau.

4 recordsLinked to original sources

arXiv2026

From Navier-Stokes to Measure-Valued Euler-Brinkman Equations: Homogenization in the Inviscid Limit

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.

math.AP↗

arXiv2026

The vanishing viscosity limit for the inhomogeneous incompressible Navier-Stokes equations around a small obstacle

We investigate the interaction between a vanishing obstacle and the vanishing viscosity limit in the setting of the inhomogeneous incompressible Navier-Stokes equations with no-slip boundary conditions. We work in the space exterior to a small obstacle in three dimensions. We prove quantitative convergence rates, assuming that the obstacle is sufficiently small, namely smaller than a constant times the viscosity. The convergence holds as long as the solution to the limit problem is known to exist and stays sufficiently smooth. This extends the results of Iftimie, Lopes Filho and Nussenzveig Lopes to the inhomogeneous Navier-Stokes equations. Moreover, we can show improved convergence rates and convergence of the gradient in $\mathbb{R}^3$.

math.AP↗

arXiv2026

Homogenization of the Navier-Stokes equations in a randomly perforated domain in the inviscid limit

We study the behaviour of the solution $u_\varepsilon$ to the Navier-Stokes equations with vanishing viscosity and a non-slip condition in a randomly perforated domain. We consider the space $\mathbb{R}^3$ where we remove $N$ holes that are i.i.d. distributed. The behaviour depends on the particle size $\varepsilon^α=N^{-α/3}$ and the viscosity $\varepsilon^γ=N^{-γ/3}$ of the fluid. We prove quantitative convergence results to a function $u$, provided that the local Reynolds number is small, in the subcritical ($α+γ>3$) and critical ($α+γ=3$) regime. In the first case, $u$ solves the Euler equations, whereas in the second case $u$ solves the Euler-Brinkman equations. This extends the results of https://doi.org/10.1088/1361-6544/acfe56 from the periodic to the random setting. We only treat the case $α>2$ so that the particles do not overlap with overwhelming probability.

math.AP↗

arXiv2024

One-dimensional inelastic collapse of four particles: asymmetric collision sequences and spherical billiard reduction

We consider a one-dimensional system of four inelastic hard spheres, colliding with a fixed restitution coefficient $r$, and we study the inelastic collapse phenomenon for such a particle system. We study a periodic, asymmetric collision pattern, proving that it can be realized, despite its instability. We prove that we can associate to the four-particle dynamical system another dynamical system of smaller dimension, acting on $\{1,2,3\} \times \mathbb{S}^2$, and that encodes the collision orders of each trajectory. We provide different representations of this new dynamical system, and study numerically its $ω$-limit sets. In particular, the numerical simulations suggest that the orbits of such a system might be quasi-periodic.

math.DS↗