Rigorous mean-field limit and cross-diffusion
The mean-field limit in a weakly interacting stochastic many-particle system for multiple
population species in the whole space is proved. The limiting system consists of cross …
population species in the whole space is proved. The limiting system consists of cross …
Weak-Strong Uniqueness for Maxwell--Stefan Systems
The weak-strong uniqueness for Maxwell--Stefan systems and some generalized systems is
proved. The corresponding parabolic cross-diffusion equations are considered in a bounded …
proved. The corresponding parabolic cross-diffusion equations are considered in a bounded …
Cross-diffusion systems with entropy structure
A Jüngel - arXiv preprint arXiv:1710.01623, 2017 - arxiv.org
Some results on cross-diffusion systems with entropy structure are reviewed. The focus is on
local-in-time existence results for general systems with normally elliptic diffusion operators …
local-in-time existence results for general systems with normally elliptic diffusion operators …
The relaxation limit of bipolar fluid models
NJ Alves, AE Tzavaras - arXiv preprint arXiv:2012.14203, 2020 - arxiv.org
This work establishes the relaxation limit from the bipolar Euler-Poisson system to the
bipolar drift-diffusion system, for data so that the latter has a smooth solution. A relative …
bipolar drift-diffusion system, for data so that the latter has a smooth solution. A relative …
High friction limit for Euler–Korteweg and Navier–Stokes–Korteweg models via relative entropy approach
GC Carnevale, C Lattanzio - Journal of Differential Equations, 2020 - Elsevier
The aim of this paper is to investigate the singular relaxation limits for the Euler–Korteweg
and the Navier–Stokes–Korteweg system in the high friction regime. We shall prove that the …
and the Navier–Stokes–Korteweg system in the high friction regime. We shall prove that the …
Asymptotic derivation of multicomponent compressible flows with heat conduction and mass diffusion
S Georgiadis, AE Tzavaras - ESAIM: Mathematical Modelling and …, 2023 - esaim-m2an.org
A Type-I model of a multicomponent system of fluids with non-constant temperature is
derived as the high-friction limit of a Type-II model via a Chapman-Enskog expansion. The …
derived as the high-friction limit of a Type-II model via a Chapman-Enskog expansion. The …
Existence and weak–strong uniqueness for Maxwell–Stefan–Cahn–Hilliard systems
A Maxwell–Stefan system for fluid mixtures with driving forces depending on Cahn–Hilliard-
type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations …
type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations …
Exponential time decay of solutions to reaction-cross-diffusion systems of Maxwell–Stefan type
The large-time asymptotics of weak solutions to Maxwell–Stefan diffusion systems for
chemically reacting fluids with different molar masses and reversible reactions are …
chemically reacting fluids with different molar masses and reversible reactions are …
Compressible multicomponent flow in porous media with Maxwell‐Stefan diffusion
L Ostrowski, C Rohde - Mathematical Methods in the Applied …, 2020 - Wiley Online Library
We introduce a Darcy‐scale model to describe compressible multicomponent flow in a fully
saturated porous medium. In order to capture cross‐diffusive effects between the different …
saturated porous medium. In order to capture cross‐diffusive effects between the different …
From nonlocal Euler-Korteweg to local Cahn-Hilliard via the high-friction limit
Several recent papers considered the high-friction limit for systems arising in fluid
mechanics. Following this approach, we rigorously derive the nonlocal Cahn-Hilliard …
mechanics. Following this approach, we rigorously derive the nonlocal Cahn-Hilliard …