Optimal time‐decay rates for the 3D compressible Magnetohydrodynamic flows with discontinuous initial data and large oscillations

2020 ◽  
Author(s):  
Guochun Wu ◽  
Yinghui Zhang ◽  
Weiyuan Zou
Keyword(s):  
Initial Data ◽  
Decay Rates ◽  
Optimal Time ◽  
Time Decay ◽  
Discontinuous Initial Data ◽  
Magnetohydrodynamic Flows ◽  
Time Decay Rates

The sharp time decay rates and stability of large solutions to the two-dimensional Phan-Thien–Tanner system with magnetic field

2021 ◽  
pp. 1-34
Author(s):  
Yuhui Chen ◽  
Minling Li ◽  
Qinghe Yao ◽  
Zheng-an Yao
Keyword(s):  
Magnetic Field ◽  
Initial Data ◽  
Convergence Rates ◽  
Splitting Method ◽  
Mhd Flow ◽  
Decay Rates ◽  
Upper And Lower Bounds ◽  
Time Decay ◽  
Large Solutions ◽  
Time Decay Rates

In this paper, we consider the magnetohydrodynamic (MHD) flow of an incompressible Phan-Thien–Tanner (PTT) fluid in two space dimensions. We focus upon the sharp time decay rates (upper and lower bounds) and global-in-time stability of large strong solutions for the PTT system with magnetic field. Firstly, the convergence of large solutions to the equilibrium have been investigated and these convergence rates are shown to be sharp. We then show that two large solutions converge globally in time as long as two initial data are close to each other. One of the main objectives of this paper is to develop a way to capture L 2 -convergence result via auxiliary logarithmic time decay estimates with the initial data in L p ( R 2 ) ∩ L 2 ( R 2 ). Improving time decay rates for the high-order derivatives of large solutions by using interpolation inequalities. In addition, time-weighted energy estimate, Fourier time-splitting method, semigroup method and iterative scheme have also been utilized.

scholarly journals Optimal time-decay rate of global classical solutions to the generalized compressible Oldroyd-B model

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Shuai Liu ◽  
Yuzhu Wang
Keyword(s):  
Decay Rate ◽  
Decay Rates ◽  
Classical Solutions ◽  
Optimal Time ◽  
Time Decay ◽  
Global Classical Solutions ◽  
Time Decay Rates ◽  
Two Space Dimensions ◽  
Time Decay Rate ◽  
Three Space

<p style='text-indent:20px;'>In this paper, we investigate the optimal time-decay rates of global classical solutions for the compressible Oldroyd-B model in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^n(n = 2,3) $\end{document}</tex-math></inline-formula>. Global classical solutions in two space dimensions are still open. We first complete the proof of global classical solutions in two space dimensions. Based on global classical solutions and Fourier spectrum analysis, we obtain the optimal time-decay rates of global classical solutions in two and three space dimensions. More precisely, if the initial data belong to <inline-formula><tex-math id="M2">\begin{document}$ L^1 $\end{document}</tex-math></inline-formula>, the optimal time-decay rate of solutions and time-decay rates of <inline-formula><tex-math id="M3">\begin{document}$ l(l = 1,\cdot\cdot\cdot,m) $\end{document}</tex-math></inline-formula> order derivatives under additional assumptions are established.</p>

scholarly journals Recent results for the logarithmic Keller-Segel-Fisher/KPP System

2019 ◽  
Vol 38 (7) ◽  
pp. 37-48
Author(s):  
Yanni Zeng ◽  
Kun Zhao
Keyword(s):  
Ground State ◽  
Decay Rates ◽  
Optimal Time ◽  
Logistic Growth ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Chemotaxis Model ◽  
Time Decay Rates ◽  
Long Time ◽  
Logarithmic Sensitivity

We consider a Keller-Segel type chemotaxis model with logarithmic sensitivity and logistic growth. It is a 2 by 2 system describing the interaction of cells and a chemical signal. We study Cauchy problem with finite initial data, i.e., without the commonly used smallness assumption on  initial perturbations around a constant ground state. We survey a sequence of recent results by the authors on  the existence of global-in-time solution,  long-time behavior, vanishing coefficient limit and optimal time decay rates of the solution.

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