A note on the long-time behavior of dissipative solutions to the Euler system

2021 ◽  
Author(s):  
Eduard Feireisl
Keyword(s):  
Euler System ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dissipative Solutions ◽  
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 On global dynamics of 2D convective Cahn–Hilliard equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Dynamics ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Initial Value ◽  
Hilliard Equation ◽  
Long Time ◽  
Cahn Hilliard Equation ◽  
Initial Boundary Value

AbstractIn this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ H 4 ( Ω ) when the initial value belongs to $H^{1}(\Omega )$ H 1 ( Ω ) .

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

Sign in / Sign up

Export Citation Format

Share Document