scholarly journals Critical Points of the $N$-vortex Hamiltonian in Bounded Planar Domains and Steady State Solutions of the Incompressible Euler Equations

2015 ◽  
Vol 75 (2) ◽  
pp. 726-744 ◽  
Author(s):  
Thomas Bartsch ◽  
Angela Pistoia
Keyword(s):  
Steady State ◽  
Euler Equations ◽  
Critical Points ◽  
Incompressible Euler Equations ◽  
Planar Domains ◽  
Steady State Solutions ◽  
Incompressible Euler

ASYMPTOTIC EXPANSIONS IN A STEADY STATE EULER–POISSON SYSTEM AND CONVERGENCE TO INCOMPRESSIBLE EULER EQUATIONS

2005 ◽  
Vol 15 (05) ◽  
pp. 717-736 ◽  
Author(s):  
YUE-JUN PENG ◽  
INGRID VIOLET
Keyword(s):  
Steady State ◽  
Euler Equations ◽  
Asymptotic Expansions ◽  
Electron Mass ◽  
Poisson System ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Incompressible Euler Equations ◽  
Potential Flows ◽  
Incompressible Euler

This work is concerned with a steady state Euler–Poisson system for potential flows arising in mathematical modeling for plasmas and semiconductors. We study the zero electron mass limit and zero relaxation time limit of the system by using the method of asymptotic expansions. These two limits are expressed by the Maxwell–Boltzmann relation and the classical drift-diffusion model, respectively. For each limit, we show the existence and uniqueness of profiles and justify the asymptotic expansions up to any order. These results also give new approaches for the convergence of the Euler–Poisson system to incompressible Euler equations, which has already been obtained via the quasi-neutral limit.

scholarly journals Convergence of a Singular Euler-Maxwell Approximation of the Incompressible Euler Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Jianwei Yang ◽  
Hongli Wang
Keyword(s):  
Euler Equations ◽  
Collisionless Plasma ◽  
Maxwell System ◽  
Energy Estimation ◽  
Incompressible Euler Equations ◽  
Incompressible Euler

This paper studies the Euler-Maxwell system which is a model of a collisionless plasma. By energy estimation and the curl-div decomposition of the gradient, we rigorously justify a singular approximation of the incompressible Euler equations via a quasi-neutral regime.

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