Initial layer and incompressible limit for Euler–Poisson equation in nonthermal plasma

2019 ◽  
Vol 29 (09) ◽  
pp. 1733-1751
Author(s):  
Tao Luo ◽  
Shu Wang ◽  
Yan-Lin Wang
Keyword(s):  
Asymptotic Expansion ◽  
Poisson Equation ◽  
Nonthermal Plasma ◽  
Approximate Solutions ◽  
Singular Limit ◽  
Incompressible Limit ◽  
Incompressible Euler Equation ◽  
Initial Layer ◽  
Compressible Euler ◽  
Incompressible Euler

The singular limit from compressible Euler–Poisson equation in nonthermal plasma to incompressible Euler equation with an ill-prepared initial data is investigated in this paper by constructing approximate solutions of the appropriate order via an asymptotic expansion. Nonlinear asymptotic stability of initial layer approximation is established with the convergence rate.

Lattice-BGK Methods for Simulating Incompressible Fluid Flows

1997 ◽  
Vol 08 (04) ◽  
pp. 793-803 ◽  
Author(s):  
Yu Chen ◽  
Hirotada Ohashi
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Poisson Equation ◽  
General Model ◽  
Incompressible Flows ◽  
Fluid Flows ◽  
Incompressible Limit ◽  
Numerical Example ◽  
Incompressible Fluid Flows

The lattice-Bhatnagar-Gross-Krook (BGK) method has been used to simulate fluid flow in the nearly incompressible limit. But for the completely incompressible flows, two special approaches should be applied to the general model, for the steady and unsteady cases, respectively. Introduced by Zou et al.,1 the method for steady incompressible flows will be described briefly in this paper. For the unsteady case, we will show, using a simple numerical example, the need to solve a Poisson equation for pressure.

Incompressible limit for the two-dimensional isentropic Euler system with critical initial data

2014 ◽  
Vol 144 (6) ◽  
pp. 1127-1154 ◽  
Author(s):  
Taoufik Hmidi ◽  
Samira Sulaiman
Keyword(s):  
Mach Number ◽  
Initial Data ◽  
Euler System ◽  
Incompressible Limit ◽  
Two Dimensional ◽  
Low Mach Number ◽  
Low Mach Number Limit ◽  
Critical Besov Space ◽  
Convergence Results ◽  
Incompressible Euler

We study the low-Mach-number limit for the two-dimensional isentropic Euler system with ill-prepared initial data belonging to the critical Besov space . By combining Strichartz estimates with the special structure of the vorticity, we prove that the lifespan of the solutions goes to infinity as the Mach number goes to zero. We also prove strong convergence results of the incompressible parts to the solution of the incompressible Euler system.

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