Convergence of the two‐fluid compressible Navier–Stokes–Poisson system to the incompressible Euler equations

2020 ◽  
Vol 43 (10) ◽  
pp. 6262-6275
Author(s):  
Young‐Sam Kwon ◽  
Fucai Li
Keyword(s):  
Euler Equations ◽  
Navier Stokes ◽  
Poisson System ◽  
Incompressible Euler Equations ◽  
Two Fluid ◽  
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.

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