Long Time Behavior of Weak Solutions to Navier–Stokes–Poisson System

2011 ◽  
Vol 14 (2) ◽  
pp. 279-294 ◽  
Author(s):  
Peter Bella
Keyword(s):  
Weak Solutions ◽  
Navier Stokes ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Poisson System ◽  
Long Time

scholarly journals TIME-DEPENDENT RESCALINGS AND LYAPUNOV FUNCTIONALS FOR THE VLASOV–POISSON AND EULER–POISSON SYSTEMS, AND FOR RELATED MODELS OF KINETIC EQUATIONS, FLUID DYNAMICS AND QUANTUM PHYSICS

2001 ◽  
Vol 11 (03) ◽  
pp. 407-432 ◽  
Author(s):  
J. DOLBEAULT ◽  
G. REIN
Keyword(s):  
Fluid Dynamics ◽  
Quantum Physics ◽  
Kinetic Equations ◽  
Euler System ◽  
Lyapunov Functionals ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Poisson System ◽  
Dispersion Effects ◽  
Long Time

We investigate rescaling transformations for the Vlasov–Poisson and Euler–Poisson systems and derive in the plasma physics case Lyapunov functionals which can be used to analyze dispersion effects. The method is also used for studying the long time behavior of the solutions and can be applied to other models in kinetic theory (two-dimensional symmetric Vlasov–Poisson system with an external magnetic field), in fluid dynamics (Euler system for gases) and in quantum physics (Schrödinger–Poisson system, nonlinear Schrödinger equation).

scholarly journals Upper Semicontinuous Property of Uniform Attractors for the 2D Nonautonomous Navier-Stokes Equations with Damping

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Xin-Guang Yang ◽  
Jun-Tao Li
Keyword(s):  
External Force ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Navier Stokes Equations ◽  
Upper Semicontinuous ◽  
Long Time ◽  
Linear Damping ◽  
Uniform Attractors

Our aim is to investigate the long-time behavior in terms of upper semicontinuous property of uniform attractors for the 2D nonautonomous Navier-Stokes equations with linear damping and nonautonomous perturbation external force, that is, the convergence of corresponding attractors when the perturbation tends to zero.

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