scholarly journals Long time behavior of solutions to the compressible MHD system in multi-dimensions

2015 ◽  
Vol 429 (2) ◽  
pp. 1033-1058 ◽  
Author(s):  
Yu-Zhu Wang ◽  
Keyan Wang
Keyword(s):  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time ◽  
Mhd System

Long time behavior of solutions to 3D generalized MHD equations

2020 ◽  
Vol 32 (4) ◽  
pp. 977-993
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Fractional Laplacian ◽  
Mhd Equations ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Algebraic Decay ◽  
Generalized Mhd Equations ◽  
Long Time ◽  
Whole Space ◽  
Mhd System ◽  
Incompressible Mhd

AbstractIn this paper, we consider the long time behavior of solutions for 3D incompressible MHD equations with fractional Laplacian. Firstly, in a periodic bounded domain, we prove the existence of a global attractor. The analysis reveals a relation between the Laplacian exponent and the regularity of the spaces of velocity and magnetic fields. Finally, in the whole space {\mathbb{R}^{3}}, we establish the sharp algebraic decay rate of solutions to the generalized MHD system provided that the parameters satisfy {\alpha,\beta\in(0,2]}.

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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