Results 1 to 10 of about 26,053 (259)

Convergence of Compressible Euler–Maxwell Equations to Incompressible Euler Equations

Communications in Partial Differential Equations, 2008
In this paper we study the combined quasineutral and non-relativistic limit of compressible Euler–Maxwell equations. For well prepared initial data the convergences of solutions of compressible Euler–Maxwell equations to the solutions of incompressible Euler equations are justified rigorously by an analysis of asymptotic expansions and a careful use of
Peng, Yue-Jun, Wang, Shu
openaire   +4 more sources

Convergence of compressible Euler–Poisson equations to incompressible type Euler equations

Asymptotic Analysis, 2005
In this paper, we study the convergence of time‐dependent Euler–Poisson equations to incompressible type Euler equations via the quasi‐neutral limit. The local existence of smooth solutions to the limit equations is proved by an iterative scheme. The method of asymptotic expansion and the symmetric hyperbolic property of the systems are used to justify
Peng, Yue-Jun, Wang, Ya-Guang
openaire   +4 more sources

The Euler–Poisswell/Darwin equation and the asymptotic hierarchy of the Euler–Maxwell equation

Asymptotic Analysis, 2023
In this paper we introduce the (unipolar) pressureless Euler–Poisswell equation for electrons as the [Formula: see text] semi-relativistic approximation and the (unipolar) pressureless Euler–Darwin equation as the [Formula: see text] semi-relativistic approximation of the (unipolar) pressureless Euler–Maxwell equation. In the “infinity-ion-mass” limit,
Möller, Jakob, Mauser, Norbert J.
openaire   +1 more source

THE EULER EQUATIONS WITH DISSIPATION

Mathematics of the USSR-Sbornik, 1993
See the review in Zbl 0766.35038.
openaire   +1 more source

On a Kinetic Formulation of the Euler Equations

SIAM Journal on Mathematical Analysis, 2015
In this article, the following Euler equations are considered over \([0,+\infty[\times \mathbb{R}^3\): \[ \begin{aligned} \partial_t \rho+\operatorname{div}(\rho u)&=0, \\ \partial_t (\rho u)+\operatorname{div}(\rho u\otimes u)+\nabla (\rho T)&=0, \\ \partial_t (\rho T)+\operatorname{div}(\rho T u)+2/3 \rho T\operatorname{div}(u)&=0.\end{aligned} \] It
openaire   +1 more source

Convergence of Compressible Euler-Maxwell Equations to Compressible Euler-Poisson Equations*

Chinese Annals of Mathematics, Series B, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Peng, Yue-Jun, Wang, Shu
openaire   +3 more sources

Convergence of the nonisentropic Euler–Maxwell equations to compressible Euler–Poisson equations

Journal of Mathematical Physics, 2009
This paper is concerned with the convergence of the time-dependent and nonisentropic Euler–Maxwell equations to compressible Euler–Poisson equations in a torus via the nonrelativistic limit. By using the method of formal asymptotic expansions, we analyze the nonrelativistic limit for periodic problems with the prepared initial data.
Yang, Jianwei, Wang, Shu
openaire   +1 more source

Euler’s Equations

2018
Euler derived the fundamental equations of an ideal fluid, that is, in the absence of friction (viscosity). They describe the conservation of momentum. We can derive from it the equation for the evolution of vorticity (Helmholtz equation). Euler’s equations have to be supplemented by the conservation of mass and by an equation of state (which relates ...
openaire   +1 more source

The ultra‐relativistic Euler equations

Mathematical Methods in the Applied Sciences, 2014
AbstractWe study the ultra‐relativistic Euler equations for an ideal gas, which is a system of nonlinear hyperbolic conservation laws. We first analyze the single shocks and rarefaction waves and solve the Riemann problem in a constructive way. Especially, we develop an own parametrization for single shocks, which will be used to derive a new explicit ...
Abdelrahman, Mahmoud A. E., Kunik, Matthias   +1 more
openaire   +1 more source

The Euler Equations

1992
The Euler equations are an approximation of the Navier-Stokes equations with the viscous forces and the volume forces being neglected. The reason for doing so is a) because viscosity and heat conduction in a gas usually play a role only in a thin layer near solid surfaces, the thickness of which is much smaller than the characteristic length of the ...
Albrecht Eberle, Arthur Rizzi, Ernst Heinrich Hirschel   +2 more
openaire   +1 more source