A rigorous proof of the zero-relaxation-time limits in the hydrodynamic equations for plasmas is given. The equations consist of the Euler equations for the electrons and/or ions coupled with a linear or nonlinear Poisson equation. The proof is based on high energy estimates for the Euler equations and appropriate compactness arguments. The theorem is valid for all adiabatic states for both ele...

4 Phenomenologi al Equation Closure. 7 4 1 Examples 8 Example: River Flow 8 Quasi-equilibrium approximation 8 Example: TraÆ Flow 9 Example: Heat Condu tion 10 Fi k's Law 10 Thermal ondu tivity, difusivity, heat equation 10 Example: Granular Flow 11 Example: Invis id Fluid Flow 12 In ompressible Euler Equations 12 In ompressible Navier-Stokes Equations 12 Gas Dynami s 13 Equation of State 13 Ise...

The three-dimensional motion of an incompressible inviscid uid is classically described by the Euler equations, but can also be seen, following Arnold 1], as a geodesic on a group of volume-preserving maps. Local existence and uniqueness of minimal geodesics have been established by Ebin and Marsden 16]. In the large, for a large class of data, the existence of minimal geodesics may fail, as sh...

We prove that any weak space-time L vanishing viscosity limit of a sequence of strong solutions of Navier-Stokes equations in a bounded domain of R satisfies the Euler equation if the solutions’ local enstrophies are uniformly bounded. We also prove that t − a.e. weak L inviscid limits of solutions of 3D Navier-Stokes equations in bounded domains are weak solutions of the Euler equation if they...

Euler equations for rotationally symmetrical motions of ideal fluid are considered. Basis of differential invariants for infinite-dimensional part of admitted group is calculated. The basis is used for construction of group foliation of Euler equations. Both automorphic and resolving systems are completed to involution. The resolving part of group foliation inherits finite-dimensional part of g...

The aim of this paper is to study the influence vorticity on existence time in fluid systems for which global smoothness and decay are known case small irrotational data. We focus two examples: Euler–Korteweg system two-fluid Euler–Maxwell system. prove that lower bound lifespan these no less than inverse Hs (s>5∕2) norm rotational part initial velocity. Our approach based energy estimates fast...

A basic example of shear flow was introduced by DiPerna and Majda to study the weak limit of oscillatory solutions of the Euler equations of incompressible ideal fluids. In particular, they proved by means of this example that weak limit of solutions of Euler equations may, in some cases, fail to be a solution of Euler equations. We use this example to provide non-generic, yet nontrivial, examp...

A compensated compactness framework is established for sonic-subsonic approximate solutions to the two-dimensional Euler equations for steady irrotational flows that may contain stagnation points. Only crude estimates are required for establishing compactness. It follows that the set of subsonic irrotational solutions to the Euler equations is compact; thus flows with sonic points over an obsta...

This article proposes and analyses distributed, leaderless, model-independent consensus algorithms for networked Euler–Lagrange systems. We propose a fundamental consensus algorithm, a consensus algorithm accounting for actuator saturation, and a consensus algorithm accounting for unavailability of measurements of generalised coordinate derivatives, for systems modelled by Euler–Lagrange equati...

One of the simplest and, at the same time, most important invariants of a topological space is the Euler characteristic. A generalization of the notion of the Euler characteristic to the equivariant setting, that is, to spaces with an action of a group (say, finite) is far from unique. An equivariant analogue of the Euler characteristic can be defined as an element of the ring of representation...