Optimal time-decay rates of the Boltzmann equation

2013 ◽  
Vol 57 (4) ◽  
pp. 807-822 ◽  
Author(s):  
MingYing Zhong
Keyword(s):  
Boltzmann Equation ◽  
Decay Rates ◽  
Optimal Time ◽  
Time Decay ◽  
The Boltzmann Equation ◽  
Time Decay Rates

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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