Related papers: Generalized hydrodynamic limit for the box-ball sy…
We consider a one-dimensional oscillatory medium with a coupling through a diffusive linear field. In the limit of fast diffusion this setup reduces to the classical Kuramoto-Battogtokh model. We demonstrate that for a finite diffusion…
This paper studies global existence, hydrodynamic limit, and large-time behavior of weak solutions to a kinetic flocking model coupled to the incompressible Navier-Stokes equations. The model describes the motion of particles immersed in a…
In this paper we are concerned with a generalized $N$-urn Ehrenfest model, where balls keeps independent random walks between $N$ boxes uniformly laid on $[0, 1]$. After a proper scaling of the transition rates function of the aforesaid…
Open problems in fluid dynamics, such as the existence of finite-time singularities (blowup), explanation of intermittency in developed turbulence, etc., are related to multi-scale structure and symmetries of underlying equations of motion.…
Two fundamental models in plasma physics are given by the Vlasov-Maxwell-Boltzmann system and the compressible Euler-Maxwell system which both capture the complex dynamics of plasmas under the self-consistent electromagnetic interactions at…
Dynamical equations in generalized hydrodynamics (GHD), a hydrodynamic theory for integrable quantum systems at the Euler scale, take a rather simple form, even though an infinite number of conserved charges are taken into account. We show…
We provide a rigorous derivation of the brownian motion as the hydrodynamic limit of a deterministic system of hard-spheres as the number of particles $N$ goes to infinity and their diameter $\varepsilon$ simultaneously goes to $0,$ in the…
We establish the vanishing viscosity limit of the Navier-Stokes equations to the Euler equations for three-dimensional compressible isentropic flow in the whole space. It is shown that there exists a unique regular solution of compressible…
Under the assumption of two fluid kinematics of a nonrelativistic Bose liquid in the presence of a local velocity field $v(x)$, local Galilei transformations are used to derive formulas for the spatial distribution of superfluidity. The…
In \cite{fgn1}, the hydrodynamic limit in the diffusive scaling of the symmetric simple exclusion process with a finite number of slow bonds of strength $n^{-\beta}$ has been studied. Here $n$ is the scaling parameter and $\beta>0$ is…
This paper concerns with the hydrodynamic limit of the Kob-Andersen model, an interacting particle system that has been introduced by physicists in order to explain glassy behavior, and widely studies since. We will see that the density…
A box-ball system is a discrete dynamical system whose dynamics come from the balls jumping according to certain rules. A permutation on n objects gives a box-ball system state by assigning its one-line notation to n consecutive boxes.…
Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…
We study a hydrodynamic limit of the Vlasov-Navier-Stokes system with external gravity force, following the framework introduced by Han-Kwan and Michel in [Han-Kwan - Michel, arXiv:2103.06668]. We answer a question raised in the latter…
We derive the linear acoustic and Stokes-Fourier equations as the limiting dynamics of a system of N hard spheres of diameter $\epsilon$ in two space dimensions, when N $\rightarrow$ $\infty$, $\epsilon$ $\rightarrow$ 0, N $\epsilon$ =…
We investigate a class of Vlasov-type kinetic flocking models featuring nonlinear velocity alignment. Our primary objective is to rigorously derive the hydrodynamic limit leading to the compressible Euler system with nonlinear alignment.…
We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…
We formulate a quantum theory of vorticity (hydro)dynamics on a general two-dimensional bosonic lattice. In the classical limit of a bosonic condensate, it reduces to conserved plasma-like vortex-antivortex dynamics. The nonlocal…
We derive the hydrodynamic limit of Glauber-Kawasaki dynamics. The Kawasaki part is simple and describes independent movement of the particles with hard core exclusive interactions. It is speeded up in a diffusive space-time scaling. The…
In the present paper we study the fast rotation limit for viscous incompressible fluids with variable density, whose motion is influenced by the Coriolis force. We restrict our analysis to two dimensional flows. In the case when the initial…