scholarly journals Notes on the space–time decay rate of the Stokes flows in the half space

2017 ◽  
Vol 263 (1) ◽  
pp. 240-263 ◽  
Author(s):  
Tongkeun Chang ◽  
Bum Ja Jin
Keyword(s):  
Decay Rate ◽  
Half Space ◽  
Space Time ◽  
Time Decay ◽  
Stokes Flows ◽  
Time Decay Rate

EARLY TIME DEPARTURES FROM THE WEISSKOPF-WIGNER DECAY RATE

1993 ◽  
Vol 08 (24) ◽  
pp. 4355-4367 ◽  
Author(s):  
K. URBANOWSKI ◽  
J. SKOREK
Keyword(s):  
Decay Rate ◽  
State Vector ◽  
Early Time ◽  
Time Decay ◽  
Time Decay Rate

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.

Time decay rate for two 3D magnetohydrodynamics- α models

2013 ◽  
Vol 37 (6) ◽  
pp. 838-845 ◽  
Author(s):  
Zaihong Jiang ◽  
Jishan Fan
Keyword(s):  
Decay Rate ◽  
Time Decay ◽  
Time Decay Rate

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 Time decay rates for the coupled modified Navier-Stokes and Maxwell equations on a half space

2021 ◽  
Vol 6 (12) ◽  
pp. 13423-13431
Author(s):  
Jae-Myoung Kim ◽  
Keyword(s):  
Decay Rate ◽  
Half Space ◽  
Spectral Decomposition ◽  
Maxwell Equations ◽  
Strong Solutions ◽  
Decay Rates ◽  
Stokes Operator ◽  
Navier Stokes ◽  
Time Decay ◽  
Time Decay Rates

<abstract><p>This paper is concerned with time decay rates of the strong solutions of an incompressible the coupled modified Navier-Stokes and Maxwell equations in a half space $ \mathbb{R}^3_+ $. With the use of the spectral decomposition of the Stokes operator and $ L^p-L^q $ estimates developed by Borchers and Miyakawa <sup>[<xref ref-type="bibr" rid="b2">2</xref>]</sup>, we study the $ L^2 $-decay rate of strong solutions.</p></abstract>

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