On the strong solutions of one-dimensional Navier-Stokes-Poisson equations for compressible non-Newtonian fluids

2013 ◽  
Vol 54 (5) ◽  
pp. 051502
Author(s):  
Yukun Song ◽  
Hongjun Yuan ◽  
Yang Chen
Keyword(s):  
Strong Solutions ◽  
Newtonian Fluids ◽  
Navier Stokes ◽  
One Dimensional ◽  
Poisson Equations

Global Solutions to the One-Dimensional Compressible Navier--Stokes--Poisson Equations with Large Data

2013 ◽  
Vol 45 (2) ◽  
pp. 547-571 ◽  
Author(s):  
Zhong Tan ◽  
Tong Yang ◽  
Huijiang Zhao ◽  
Qingyang Zou
Keyword(s):  
Global Solutions ◽  
Large Data ◽  
Navier Stokes ◽  
One Dimensional ◽  
Poisson Equations ◽  
The One

Asymptotics toward a nonlinear wave for an outflow problem of a model of viscous ions motion

2017 ◽  
Vol 27 (11) ◽  
pp. 2111-2145 ◽  
Author(s):  
Yeping Li ◽  
Peicheng Zhu
Keyword(s):  
Nonlinear Wave ◽  
The Self ◽  
Navier Stokes ◽  
Asymptotically Stable ◽  
Spatial Decay ◽  
Main Ingredient ◽  
One Dimensional ◽  
Poisson Equations ◽  
Self Consistent ◽  
The One

We shall investigate the asymptotic stability, toward a nonlinear wave, of the solution to an outflow problem for the one-dimensional compressible Navier–Stokes–Poisson equations. First, we construct this nonlinear wave which, under suitable assumptions, is the superposition of a stationary solution and a rarefaction wave. Then it is shown that the nonlinear wave is asymptotically stable in the case that the initial data are a suitably small perturbation of the nonlinear wave. The main ingredient of the proof is the [Formula: see text]-energy method that takes into account both the effect of the self-consistent electrostatic potential and the spatial decay of the stationary part of the nonlinear wave.

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