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Convergence of Compressible Euler-Maxwell Equations to Compressible Euler-Poisson Equations*
Chinese Annals of Mathematics, Series B, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Peng, Yue-Jun, Wang, Shu
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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 ...
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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 ...
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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 +2 more
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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 +2 more
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Convergence of the nonisentropic Euler–Maxwell equations to compressible Euler–Poisson equations
Journal of Mathematical Physics, 2009This 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
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The ultra‐relativistic Euler equations
Mathematical Methods in the Applied Sciences, 2014AbstractWe 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. +1 more
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2014
This chapter presents Euler equation without and with the presence of a magnetic field. The equation is written in both spherical and cylindrical coordinates, and applied to a stellar envelope. Some examples involving the solar wind are given, and a discussion is presented on the escape velocity from stars.
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This chapter presents Euler equation without and with the presence of a magnetic field. The equation is written in both spherical and cylindrical coordinates, and applied to a stellar envelope. Some examples involving the solar wind are given, and a discussion is presented on the escape velocity from stars.
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1984
One of the most important applications of Newtonian mechanics occurs in the study of the motion of a rigid body. To apply Newtonian principles to a system of particles rigidly attached to each other is by no means trivial; and when the mathematization of the problem has been carried out, the differential equations which result are among the most ...
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One of the most important applications of Newtonian mechanics occurs in the study of the motion of a rigid body. To apply Newtonian principles to a system of particles rigidly attached to each other is by no means trivial; and when the mathematization of the problem has been carried out, the differential equations which result are among the most ...
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2017
Following [36], we shall develop the theory on the real line, although many of the results can be extended to \(\mathbf{R}^{n}\).
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Following [36], we shall develop the theory on the real line, although many of the results can be extended to \(\mathbf{R}^{n}\).
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On the Equation of Euler–Poisson–Darboux
SIAM Journal on Mathematical Analysis, 1973Weak solutions of the initial value problem for the EPD equation are constructed using distributional methods. After taking the Fourier transform with respect to the space variables we obtain an equation related to the Bessel differential equation which can easily be solved.
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