Non-existence of global solutions to Euler-Poisson equations for repulsive forces

1990 ◽  
Vol 7 (2) ◽  
pp. 363-367 ◽  
Author(s):  
Benoît Perthame
Keyword(s):  
Global Solutions ◽  
Poisson Equations ◽  
Repulsive Forces

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

scholarly journals Improved blowup results for the Euler and Euler–Poisson equations with repulsive forces

2014 ◽  
Vol 417 (1) ◽  
pp. 57-64 ◽  
Author(s):  
Rui Li ◽  
Xing Lin ◽  
Zongwei Ma ◽  
Jingjun Zhang
Keyword(s):  
Poisson Equations ◽  
Repulsive Forces

scholarly journals Stabilities for Nonisentropic Euler-Poisson Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Ka Luen Cheung ◽  
Sen Wong
Keyword(s):  
Energy Method ◽  
Finite Time ◽  
Blow Up ◽  
Classical Solutions ◽  
Poisson Equations ◽  
Repulsive Forces

We establish the stabilities and blowup results for the nonisentropic Euler-Poisson equations by the energy method. By analysing the second inertia, we show that the classical solutions of the system with attractive forces blow up in finite time in some special dimensions when the energy is negative. Moreover, we obtain the stabilities results for the system in the cases of attractive and repulsive forces.

scholarly journals Blow up for the solutions of the pressureless Euler-Poisson equations with time-dependent damping

2021 ◽  
Author(s):  
Jianli Liu ◽  
Jingwei Wang ◽  
Lining Tong
Keyword(s):  
Plasma Physics ◽  
Formation Mechanism ◽  
Blow Up ◽  
Time Dependent ◽  
Singularity Formation ◽  
Poisson Equations ◽  
Repulsive Forces ◽  
Physical Phenomena ◽  
Semiconductor Modeling

The Euler-Poisson equations can be used to describe the important physical phenomena in many areas, such as semiconductor modeling and plasma physics. In this paper, we show the singularity formation mechanism for the solutions of the pressureless Euler-Poisson equations with time-dependent damping for the attractive forces in R^n (n ≧1) and the repulsive forces in R. We obtain the blow up of the derivative of the velocity under the appropriate assumptions.

scholarly journals Global existence of weak solution for the compressible Navier–Stokes–Poisson system with density-dependent viscosity

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Meiying Cui ◽  
Wenjing Song
Keyword(s):  
Global Solutions ◽  
Approximate Solutions ◽  
Doping Profile ◽  
Navier Stokes ◽  
Density Dependent ◽  
Poisson Equations ◽  
Viscosity Coefficients ◽  
Approximate System ◽  
Dependent Viscosity ◽  
Entropy Estimates

Abstract In this paper, we are concerned with the existence of global weak solutions to the compressible Navier–Stokes–Poisson equations with the non-flat doping profile when the viscosity coefficients are density-dependent, the data are large and spherically symmetric, and we focus on the case where those coefficients vanish in vacuum. We construct a suitable approximate system and consider it in annular regions between two balls. The global solutions are obtained as limits of such approximate solutions. Our proofs are mainly based on the energy and entropy estimates.

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