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The purpose of this article is to study extrapolation of solvability for boundary value problems of elliptic systems in divergence form on the upper half-space assuming De Giorgi type conditions. We develop a method allowing to treat each…
We rigorously justify the bilayer shallow-water system as an approximation to the hydrostatic Euler equations in situations where the flow is density-stratified with close-to-piecewise constant density profiles, and close-to-columnar…
We study a generalization of the Navier-Stokes-Fourier system for an incompressible fluid where the deviatoric part of the Cauchy stress tensor is related to the symmetric part of the velocity gradient via a maximal monotone 2-graph that is…
This paper is devoted to the study of the low Mach number limit for the 2D isentropic Euler system associated to ill-prepared initial data with slow blow up rate on $\log\varepsilon^{-1}$. We prove in particular the strong convergence to…
In this paper, we study the dynamics of a finite number of spherical bubbles in a compressible fluid within a bounded open domain of R 3 . The fluid-bubble interaction is described by a system of nonlinear partial differential equations…
Understanding the relaxation of a system towards equilibrium is a longstanding problem in statistical mechanics. Here we address the role of long-range interactions in this process by considering a class of two-dimensional or geophysical…
This paper proposes a new approach to solving the Buckley-Leverett System, which is to consider a compressible approximation model characterized by a stiff pressure law. Passing to the incompressible limit, the compressible model gives rise…
We derive the incompressible Euler equations with heat convection with the no-penetration boundary condition from the Boltzmann equation with the diffuse boundary in the hydrodynamic limit for the scale of large Reynold number. Inspired by…
We consider the free boundary problem for the Euler--Fourier system that describes the motion of compressible, inviscid and heat-conducting fluids. The effect of surface tension is neglected and there is no heat flux across the free…
The Busenberg--Travis cross-diffusion system for segregating populations is approximated by the compressible Navier--Stokes--Korteweg equations on the torus, including a density-dependent viscosity and drag forces. The Korteweg term can be…
We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding…
We propose and analyze a one-dimensional multi-species cross-diffusion system with non-zero-flux boundary conditions on a moving domain, motivated by the mod- eling of a Physical Vapor Deposition process. Using the boundedness by entropy…
The dynamics of a degree of freedom associated to an axial vector in contact with a heat bath is decribed by means of a probability distribution function obeying a Fokker-Planck equation. The equation is derived by using mesoscopic…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
In a recent Letter [1] a framework for estimating entropy was introduced and applied to one-dimensional and two-dimensional systems. In this Comment we show that the method is not well suited for estimating entropy in bidimensional systems…
One-dimensional hard rod gases are explicitly constructed as the limits of discrete systems: exclusion processes involving particles of arbitrary length. Those continuum many-body systems in general do not exhibit the same hydrodynamic…
We study the finite element formulation of general boundary conditions for incompressible flow problems. Distinguishing between the contributions from the inviscid and viscid parts of the equations, we use Nitsche's method to develop a…
A compactness framework is established for approximate solutions to subsonic-sonic flows governed by the steady full Euler equations for compressible fluids in arbitrary dimension. The existing compactness frameworks for the two-dimensional…
In this paper we give an elementary proof of uniqueness of solutions to a gas-disk interaction system with diffusive boundary condition. Existence of near-equilibrium solutions for this type of systems with various boundary conditions has…
We establish a general perturbative method to prove entropic Ricci curvature bounds for interacting stochastic particle systems. We apply this method to obtain curvature bounds in several examples, namely: Glauber dynamics for a class of…