Publications

2025

• Applications of new boundary conditions for the Boltzmann equation derived from a kinetic model of gas-surface interaction
  
  • Kosuge Shingo
  • Aoki Kazuo
  • Giovangigli Vincent
  • Golse François
  , 2024. Recently, new models of the boundary condition for the Boltzmann equation were proposed on the basis of a kinetic model of gas-surface interactions [K. Aoki et.al., Phys. Rev. E 106(3), 035306 (2022)]. In the present paper, the kernel representations of the models are given, and the models are applied to some basic problems of a rarefied gas between two parallel plates. To be more specific, the heat-transfer between the plates with different temperatures, plane Couette flow, and plane Poiseuille flow driven by an external force are numerically investigated by using the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation and the new models of the boundary condition. The results are compared with those based on the conventional Maxwell-type boundary conditions.
• Parallel approximation of the exponential of semidefinite negative Hermitian matrices
  
  • Hecht Frédéric
  • Kaber Sidi-Mahmoud
  • Perrin Lucas
  • Plagne Alain
  • Salomon Julien
  , 2025. The numerical solution of parabolic equations often involves calcu- lating the exponential of Hermitian matrices. In this work, we consider a rational approximation of the exponential function to design an algorithm for computing the matrix exponential in the Hermitian case. Using partial fraction decomposition, we derive a parallelizable method, reducing the computation to independent reso- lutions of linear systems. We analyze the effects of rounding errors on the accuracy of our algorithm. This work is complemented by numerical tests that demonstrate the efficiency of our method and compare its performance with standard implemen- tations.
• Semi-classical limit of the massive Klein-Gordon-Maxwell system toward the relativistic Euler-Maxwell system via an adapted modulated energy method
  
  • Salvi Tony
  , 2025. We show that the momentum, the density, and the electromagnetic field associated with the massive Klein-Gordon-Maxwell equations converge in the semi-classical limit towards their respective equivalents associated with the relativistic Euler-Maxwell equations. The proof relies on a modulated stress-energy method and a compactness argument. We also give a proof of the well-posedness of the relativistic Euler-Maxwell equations and show how this system, and so the semi-classical limit of Klein-Gordon-Maxwell, is related to the relativistic massive Vlasov-Maxwell equations. (10.48550/arXiv.2502.06622)
  DOI : 10.48550/arXiv.2502.06622
• The Davenport constant of balls and boxes
  
  • Girard Benjamin
  • Plagne Alain
  , 2025. Given an additively written abelian group $G$ and a set $X\subseteq G$, we let $\mathsf{D}(X)$ denote the Davenport constant of $X$, namely the largest non-negative integer $n$ for which there exists a sequence $x_1, \dots, x_n$ of elements of $X$ such that $\sum_{i=1}^n x_i =0$ and $\sum_{i \in I} x_i \ne 0$ for each non-empty proper subset $I$ of $\{1, \ldots, n\}$. In this paper, we mainly investigate the case when $G$ is $\mathbb{Z}^2$ and $\mathbb{Z}^3$, and $X$ is a discrete Euclidean ball. An application to the classical problem of estimating the Davenport constant of a box - a product of intervals of integers - is then obtained.
• The Davenport constant of an interval: a proof that $\mathsf{D}= \chi$
  
  • Girard Benjamin
  • Plagne Alain
  , 2025. For two positive integers $m$ and $M$, we study the Davenport constant of the interval of integers $[\![ -m,M ]\!]$, that is the maximal length of a minimal zero-sum sequence composed of elements from $[\![ -m,M ]\!]$. We prove the conjecture that it is equal to $m+M- r$ where $r$ is the smallest integer which can be decomposed as a sum of two non-negative integers $t_1$ and $t_2$ ($r=t_1+t_2$) having the property that $\gcd (M-t_1, m-t_2)=1$.
• The Navier-Stokes limit of kinetic equations for low regularity data
  
  • Carrapatoso Kleber
  • Gallagher Isabelle
  • Tristani Isabelle
  Tunisian Journal of Mathematics, Mathematical Science Publishers, 2025. In this paper, we investigate the link between kinetic equations (including Boltzmann with or without cutoff assumption and Landau equations) and the incompressible Navier-Stokes equation. We work with strong solutions and we treat all the cases in a unified framework. The main purpose of this work is to be as accurate as possible in terms of functional spaces. More precisely, it is well-known that the Navier-Stokes equation can be solved in a lower regularity setting (in the space variable) than kinetic equations. Our main result allows to get a rigorous link between solutions to the Navier-Stokes equation with such low regularity data and kinetic equations.