The sharp time decay rate of the isentropic Navier-Stokes system in <inline-formula><tex-math id="M1">\begin{document}$ {\mathop{\mathbb R\kern 0pt}\nolimits}^3 $\end{document}</tex-math></inline-formula>

The problem of the early time decay rate is studied using the equation for a projection of a state vector. Formulas are found for the decay rate γ(t), generally depending on time, and for early time departures of γ(t) from a rate γ0, given by Weisskopf-Wigner approximation. It is shown that γ(t)→0 as t→0, and γ(t)→γ0 as t→∞. The dependence γ(t) on t is studied numerically in some models.

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Time decay rate of weak solutions to the generalized MHD equations in R2

Applied Mathematics and Computation ◽

10.1016/j.amc.2016.07.028 ◽

2017 ◽

Vol 292 ◽

pp. 1-8

Author(s):

Caidi Zhao ◽

Bei Li

Keyword(s):

Decay Rate ◽

Weak Solutions ◽

Mhd Equations ◽

Time Decay ◽

Generalized Mhd Equations ◽

Time Decay Rate

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Upper and lower bounds of time decay rate of solutions to a class of incompressible third grade fluid equations

Nonlinear Analysis Real World Applications ◽

10.1016/j.nonrwa.2013.08.001 ◽

2014 ◽

Vol 15 ◽

pp. 229-238 ◽

Cited By ~ 16

Author(s):

Caidi Zhao ◽

Yunyun Liang ◽

Min Zhao

Keyword(s):

Decay Rate ◽

Lower Bounds ◽

Third Grade ◽

Upper And Lower Bounds ◽

Time Decay ◽

Third Grade Fluid ◽

Fluid Equations ◽

Grade Fluid ◽

Time Decay Rate

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Time decay rate for two 3D magnetohydrodynamics- α models

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.2840 ◽

2013 ◽

Vol 37 (6) ◽

pp. 838-845 ◽

Cited By ~ 6

Author(s):

Zaihong Jiang ◽

Jishan Fan

Keyword(s):

Decay Rate ◽

Time Decay ◽

Time Decay Rate

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

Evolution Equations and Control Theory ◽

10.3934/eect.2021041 ◽

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>

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