scholarly journals Global Existence and Optimal Decay Rates for Three-Dimensional Compressible Viscoelastic Flows System with Damping

2018 ◽  
Vol 06 (11) ◽  
pp. 2273-2294
Author(s):  
Wenfeng Xu
Keyword(s):  
Global Existence ◽  
Three Dimensional ◽  
Decay Rates ◽  
Viscoelastic Flows ◽  
Optimal Decay Rates ◽  
Optimal Decay

Global well-posedness and decay estimates for three-dimensional compressible Navier–Stokes–Allen–Cahn systems

2021 ◽  
pp. 1-32
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Three Dimensional ◽  
Decay Rates ◽  
Navier Stokes ◽  
Small Data ◽  
Well Posedness ◽  
Optimal Decay Rates ◽  
Optimal Decay ◽  
The Cauchy Problem ◽  
Time Decay Rates ◽  
Derivatives Of

We study the small data global well-posedness and time-decay rates of solutions to the Cauchy problem for three-dimensional compressible Navier–Stokes–Allen–Cahn equations via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained, the $\dot {H}^{-s}$ ( $0\leq s<\frac {3}{2}$ ) negative Sobolev norms is shown to be preserved along time evolution and enhance the decay rates.

scholarly journals Global well-posedness and optimal time decay rates of solutions to the three-dimensional magneto-micropolar fluid equations

2021 ◽  
Author(s):  
Dongjuan Niu ◽  
Haifeng Shang
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Besov Spaces ◽  
Micropolar Fluid ◽  
Three Dimensional ◽  
Decay Rates ◽  
Decay Estimates ◽  
Optimal Decay ◽  
Fluid Equations ◽  
Micropolar Fluid Equations

This paper deals with the global existence and decay estimates of solutions to the three-dimensional magneto-micropolar fluid equations with only velocity dissipation and magnetic diffusion in the whole space with various Sobolev and Besov spaces. Specifically, we first investigate the global existence and optimal decay estimates of weak solutions. Then we prove the global existence of solutions with small initial data in $H^s$, $B_{2, \infty}^s$ and critical Besov spaces, respectively. Furthermore, the optimal decay rates of these global solutions are correspondingly established in $\dot{H}^m$ and $\dot{B}_{2, \infty}^m$ spaces with $0\leq m\leq s$ and in $\dot{B}_{2, 1}^{m}$ with $0\leq m\leq \frac 12$, when the initial data belongs to $\dot{B}_{2, \infty}^{-l}$ ($0< l\leq\frac32$). The main difficulties lie in the presence of linear terms and the lack of micro-rotation velocity dissipation. To overcome them, we make full use of the special structure of the system and employ various techniques involved with the energy methods, the improved Fourier splitting, Fourier analysis and the regularity interpolation methods.

scholarly journals Optimal decay rates for the compressible viscoelastic flows

2016 ◽  
Vol 57 (11) ◽  
pp. 111506 ◽  
Author(s):  
Yin Li ◽  
Ruiying Wei ◽  
Zheng-an Yao
Keyword(s):  
Decay Rates ◽  
Viscoelastic Flows ◽  
Optimal Decay Rates ◽  
Optimal Decay
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