scholarly journals A remark about global existence for the Navier-Stokes-Poisson system

1999 ◽  
Vol 12 (7) ◽  
pp. 31-37 ◽  
Author(s):  
B. Ducomet
Keyword(s):  
Global Existence ◽  
Navier Stokes ◽  
Poisson System

SOME ASYMPTOTICS FOR A REACTIVE NAVIER–STOKES–POISSON SYSTEM

1999 ◽  
Vol 09 (07) ◽  
pp. 1039-1076 ◽  
Author(s):  
B. DUCOMET
Keyword(s):  
Global Existence ◽  
Global Solution ◽  
Spherical Model ◽  
Navier Stokes ◽  
Positive Energy ◽  
Stability Of Solutions ◽  
Poisson System ◽  
Rigid Core ◽  
Existence And Stability

We prove global existence and stability of solutions for a spherical model of reactive compressible self-gravitating fluid when a rigid core is present. In the absence of core, we show that no global solution of positive energy can exist.

scholarly journals Global Existence and Asymptotic Behavior of Self-Similar Solutions for the Navier-Stokes-Nernst-Planck-Poisson System in

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Jihong Zhao ◽  
Chao Deng ◽  
Shangbin Cui
Keyword(s):  
Global Existence ◽  
Dimensional Space ◽  
System Modeling ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Poisson System ◽  
Small Initial Data ◽  
The Cauchy Problem ◽  
Self Similar ◽  
Similar Solutions

We study the Navier-Stokes-Nernst-Planck-Poisson system modeling the flow of electrohydrodynamics. For small initial data, the global existence, uniqueness, and asymptotic stability as time goes to infinity of self-similar solutions to the Cauchy problem of this system posed in the whole three dimensional space are proved in the function spaces of pseudomeasure type.

scholarly journals GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO

2011 ◽  
Vol 21 (03) ◽  
pp. 421-457 ◽  
Author(s):  
RAPHAËL DANCHIN ◽  
MARIUS PAICU
Keyword(s):  
Global Existence ◽  
Turbulent Flows ◽  
Vertical Direction ◽  
Boussinesq System ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Incompressible Euler Equation ◽  
Navier Stokes Equation ◽  
Transport Diffusion ◽  
Anisotropic Viscosity

Models with a vanishing anisotropic viscosity in the vertical direction are of relevance for the study of turbulent flows in geophysics. This motivates us to study the two-dimensional Boussinesq system with horizontal viscosity in only one equation. In this paper, we focus on the global existence issue for possibly large initial data. We first examine the case where the Navier–Stokes equation with no vertical viscosity is coupled with a transport equation. Second, we consider a coupling between the classical two-dimensional incompressible Euler equation and a transport–diffusion equation with diffusion in the horizontal direction only. For both systems, we construct global weak solutions à la Leray and strong unique solutions for more regular data. Our results rest on the fact that the diffusion acts perpendicularly to the buoyancy force.

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