Long Time Behavior of Solutions to the 3D Compressible Euler Equations with Damping

2003 ◽  
Vol 28 (3-4) ◽  
pp. 795-816 ◽  
Author(s):  
Thomas C. Sideris ◽  
Becca Thomases ◽  
Dehua Wang
Keyword(s):  
Euler Equations ◽  
Compressible Euler Equations ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Compressible Euler ◽  
Long Time

scholarly journals Global Existence and Long-Time Behavior of Solutions to the Full Compressible Euler Equations with Damping and Heat Conduction in ℝ 3

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Yunshun Wu ◽  
Yong Wang ◽  
Rong Shen
Keyword(s):  
Heat Conduction ◽  
Euler Equations ◽  
Three Dimensional ◽  
Compressible Euler Equations ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Algebraic Decay ◽  
Compressible Euler ◽  
The Cauchy Problem ◽  
Long Time

We study the Cauchy problem of the three-dimensional full compressible Euler equations with damping and heat conduction. We prove the existence and uniqueness of the global small H N N ≥ 3 solution; in particular, we only require that the H 4 norms of the initial data be small when N ≥ 5 . Moreover, we use a pure energy method to show that the global solution converges to the constant equilibrium state with an optimal algebraic decay rate as time goes to infinity.

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.

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