Related papers: Onsager relations and Eulerian hydrodynamics for s…
Because scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action, they do not lead to conservation laws. Instead, an extension of Noether's theorem reduces the equations of motion to…
Hyperbolic conservation laws posed on manifolds arise in many applications to geophysical flows and general relativity. Recent work by the author and his collaborators attempts to set the foundations for a study of weak solutions defined on…
We are concerned with a new solution formula and its applications to the analysis of properties of entropy solutions of the Cauchy problem for one-dimensional scalar hyperbolic conservation laws, wherein the flux functions exhibit convexity…
Systems of the first order partial differential equations with singular solutions appear in many multiphysics problems and the weak formulation of solutions involve in many cases product of distributions. In this paper we study such a…
We rigorously show a large friction limit of hydrodynamic models with alignment, attractive, and repulsive effects. More precisely, we consider pressureless Euler equations with nonlocal forces and provide a quantitative estimate of large…
This article is concerned with the dynamics of a mixture of gases. Under the assumption that all the gases are isothermal and inviscid, we show that the governing equations have an elegant conservation-dissipation structure. With the help…
On the example of two-phase continua experiencing stress induced solid-fluid phase transitions we explore the use of the Euler structure in the formulation of the governing equations. The Euler structure guarantees that solutions of the…
We study the limiting behavior of the solutions of Euler equations of one-dimensional compressible fluid flow as the pressure like term vanishes. This system can be thought of as an approximation for the one dimensional model for large…
We prove almost sure Euler hydrodynamics for a large class of attractive particle systems on $\Z$ starting from an arbitrary initial profile. We generalize earlier works by Sepp\"al\"ainen (1999) and Andjel et al. (2004). Our constructive…
In this letter we clarify the role of heat flux in the hydrodynamic balance equations in 2D quantum wells, facilitating the formulation of an Onsager relation within the framework of this theory. We find that the Onsager relation is…
The Heisenberg dynamics of the energy, momentum, and particle densities for fermions with short-range pair interactions is shown to converge to the compressible Euler equations in the hydrodynamic limit. The pressure function is given by…
We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the non-relativistic incompressible Euler equation. For viscous…
This paper addresses the problem of energy conservation for the two- and three-dimensional density-dependent Euler equations. Two types of sufficient conditions on the regularity of solutions are provided to ensure the conservation of total…
We present a new hydrodynamic model consisting of the pressureless Euler equations and the isentropic compressible Navier-Stokes equations where the coupling of two systems is through the drag force. This coupled system can be derived, in…
We consider some interacting particle processes with long-range dynamics: the zero-range and exclusion processes with long jumps. We prove that the hydrodynamic limit of these processes corresponds to a (possibly non-linear) fractional heat…
We study the diffusive scaling limit for a chain of $N$ coupled oscillators. In order to provide the system with good ergodic properties, we perturb the Hamiltonian dynamics with random flips of velocities, so that the energy is locally…
The properties of dense granular systems are analyzed from a hydrodynamical point of view, based on conservation laws for the particle number density and linear momentum. We discuss averaging problems associated with the nature of such…
We present a general, model-independent, quantum statistical treatment of the connection between the quantum and hydrodynamical pictures of reservoir driven macroscopic systems. This treatment is centred on the large scale properties of…
In this paper I present a pedagogical derivation of continuity equations manifesting exact conservation laws in an interacting electronic system based on the nonequilibrium Keldysh technique. The purpose of this exercise is to lay the…
Isolated quantum systems follow the unitary evolution, which guarantees the full many body state always keeps a constant entropy as its initial one. In comparison, the local subsystems exhibit relaxation behavior and evolve towards certain…