Existence and stability of stationary solutions to the compressible Navier–Stokes–Poisson equations

2016 ◽  
Vol 32 ◽  
pp. 260-293 ◽  
Author(s):  
Hong Cai ◽  
Zhong Tan
Keyword(s):  
Stationary Solutions ◽  
Navier Stokes ◽  
Poisson Equations ◽  
Existence And Stability

Blow-up for the compressible isentropic Navier-Stokes-Poisson equations

2019 ◽  
Vol 70 (1) ◽  
pp. 9-19
Author(s):  
Jianwei Dong ◽  
Junhui Zhu ◽  
Yanping Wang
Keyword(s):  
Blow Up ◽  
Navier Stokes ◽  
Poisson Equations

Existence and stability of static shells for the Vlasov–Poisson system

Analysis ◽  
2006 ◽  
Vol 26 (4) ◽  
Author(s):  
Achim Schulze
Keyword(s):  
Spherical Symmetry ◽  
Variational Approach ◽  
Stationary Solutions ◽  
Poisson System ◽  
Existence And Stability

We prove the existence and stability of stationary solutions to the Vlasov–Poisson System with spherical symmetry, which describe static shells, i.e., the support of their densities is bounded away from the origin. We use a variational approach which was established by Y. Guo and G. Rein.

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 Initial boundary value problems for the three-dimensional compressible elastic Navier-Stokes-Poisson equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1356-1383
Author(s):  
Yong Wang ◽  
Wenpei Wu
Keyword(s):  
Equilibrium State ◽  
Boundary Value Problems ◽  
Electrostatic Potential ◽  
Boundary Value ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Navier Stokes ◽  
Initial Boundary Value Problems ◽  
Poisson Equations ◽  
Initial Boundary Value

Abstract We study the initial-boundary value problems of the three-dimensional compressible elastic Navier-Stokes-Poisson equations under the Dirichlet or Neumann boundary condition for the electrostatic potential. The unique global solution near a constant equilibrium state in H 2 space is obtained. Moreover, we prove that the solution decays to the equilibrium state at an exponential rate as time tends to infinity. This is the first result for the three-dimensional elastic Navier-Stokes-Poisson equations under various boundary conditions for the electrostatic potential.

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