The optimal temporal decay estimates for the micropolar fluid system in negative Fourier–Besov spaces

2019 ◽  
Vol 475 (1) ◽  
pp. 154-172 ◽  
Author(s):  
Weipeng Zhu ◽  
Jihong Zhao
Keyword(s):  
Besov Spaces ◽  
Micropolar Fluid ◽  
Decay Estimates ◽  
Fluid System ◽  
Temporal Decay

The optimal decay estimates on the framework of Besov spaces for the Euler–Poisson two-fluid system

2015 ◽  
Vol 25 (10) ◽  
pp. 1813-1844 ◽  
Author(s):  
Jiang Xu ◽  
Shuichi Kawashima
Keyword(s):  
Besov Spaces ◽  
Hyperbolic Systems ◽  
Low Frequency ◽  
Direct Consequence ◽  
Decay Rates ◽  
Decay Estimates ◽  
Fluid System ◽  
Optimal Decay Rates ◽  
Optimal Decay ◽  
Two Fluid

In this paper, we are concerned with the optimal decay estimates for the Euler–Poisson two-fluid system. It is first revealed that the irrotationality of the coupled electronic field plays a key role such that the two-fluid system has the same dissipative structure as generally hyperbolic systems satisfying the Shizuta–Kawashima condition. This fact inspires us to obtain decay properties for linearized systems in the framework of Besov spaces. Furthermore, various decay estimates of solution and its derivatives of fractional order are deduced by time-weighted energy approaches in terms of low-frequency and high-frequency decompositions. As the direct consequence, the optimal decay rates of Lp(ℝ3)-L2 (ℝ3) (1 ≤ p < 2) type for the Euler–Poisson two-fluid system are also shown. Compared with previous works in Sobolev spaces, a new observation is that the difference of variables exactly consists of a one-fluid Euler–Poisson equations, which leads to the sharp decay estimates for velocities.

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.

Long-time behaviour for porous medium equations with convection

1998 ◽  
Vol 128 (2) ◽  
pp. 315-336 ◽  
Author(s):  
Ph. Laurençot ◽  
F. Simondon
Keyword(s):  
Porous Medium ◽  
Real Line ◽  
Integrable Function ◽  
Time Profile ◽  
Decay Estimates ◽  
Time Behaviour ◽  
Temporal Decay ◽  
Long Time Behaviour ◽  
Long Time ◽  
Porous Medium Equations

Long-time behaviour of solutions to porous medium equations with convection is investigated when the initial datum is a non-negative and integrable function on the real line. The long-time profile of the solutions is determined, and depends on whether the convective or the diffusive effect dominates for large times. Sharp temporal decay estimates are also provided.

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