Related papers: Relative Entropy Method for the relaxation limit o…
A semi-implicit in time, entropy stable finite volume scheme for the compressible barotropic Euler system is designed and analyzed and its weak convergence to a dissipative measure-valued (DMV) solution [E. Feireisl et al., Dissipative…
We propose a BGK-type kinetic model for a binary gas mixture, designed to serve as a kinetic formulation of compressible two-phase fluid dynamics. The model features species-dependent adiabatic exponents, and the relaxation operator is…
We show that weak solutions of degenerate Navier-Stokes equations converge to the strong solutions of the pressureless Euler system with linear drag term, Newtonian repulsion and quadratic confinement. The proof is based on the relative…
For the incompressible and the isentropic compressible Euler equations in arbitrary space dimension, we establish the principle of localised relative energy, thus generalising the well-known relative energy method. To this end, we adapt…
This paper studies the global existence and uniqueness of strong solutions and its large-time behavior for the compressible isothermal Euler equations with a nonlocal dissipation. The system is rigorously derived from the kinetic…
We are concerned with the global existence of finite-energy entropy solutions of the one-dimensional compressible Euler equations with (possibly) damping, alignment forces, and nonlocal interactions: Newtonian repulsion and quadratic…
We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence…
We propose a new model which describes relativistic hydrodynamics and generalizes the standard Euler system of isentropic perfect fluids. Remarkably, our system admits a convex extension which allows us to transform it to a symmetric…
Hydrodynamic systems arising in swarming modelling include nonlocal forces in the form of attractive-repulsive potentials as well as pressure terms modelling strong local repulsion. We focus on the case where there is a balance between…
In this paper, the main objective is to generalize to the Navier-Stokes-Korteweg (with density dependent viscosities satisfying the BD relation) and Euler-Korteweg systems a recent relative entropy [proposed by D. Bresch, P. Noble and…
The main objective of this paper is to prove that if capillarity effect is taken into account then there exist dissipative solutions to a system describing viscoplastic compressible flows with density dependent viscosities in a periodic…
We propose and study a nonlocal Euler system with relaxation, which tends to a strictly hyperbolic system under the hyperbolic scaling limit. An independent proof of the local existence and uniqueness of this system is presented in any…
This work concerns the numerical approximation with a finite volume method of inviscid, nonequilibrium, high-temperature flows in multiple space dimensions. It is devoted to the analysis of the numerical scheme for the approximation of the…
We consider the kinetic Cucker-Smale model with local alignment as a mesoscopic description for the flocking dynamics. The local alignment was first proposed by Karper, Mellet and Trivisa \cite{K-M-T-3}, as a singular limit of a normalized…
This paper investigates the diffusion limit of a kinetic BGK-type equation, focusing on its relaxation to a nonlinear aggregation-diffusion equation, where the diffusion exhibits a porous-medium-type nonlinearity. Unlike previous studies by…
We present two types of the hydrodynamic limit of the nonlinear Schr\"odinger-Chern-Simons (SCS) system. We consider two different scalings of the SCS system and show that each SCS system asymptotically converges towards the compressible…
Several recent papers considered the high-friction limit for systems arising in fluid mechanics. Following this approach, we rigorously derive the nonlocal Cahn-Hilliard equation as a limit of the nonlocal Euler-Korteweg equation using the…
The hydrodynamic limit of a kinetic Cucker-Smale model is investigated. In addition to the free-transport of individuals and the Cucker-Smale alignment operator, the model under consideration includes a strong local alignment term. This…
In this paper we study a local and a non-local regularization of the system of nonlinear elastodynamics with a non-convex energy. We show that solutions of the non-local model converge to those of the local model in a certain regime. The…
We study the hydrodynamic limit of the nonisothermal BGK model toward smooth Euler Maxwellians. For a prescribed smooth Euler solution, we derive a relative entropy stability estimate between a BGK solution and the associated Maxwellian.…