Energy Decay Rate of the Wave Equations on Riemannian Manifolds with Critical Potential

2017 ◽  
Vol 78 (1) ◽  
pp. 61-101
Author(s):  
Yuxiang Liu ◽  
Peng-Fei Yao
Keyword(s):  
Decay Rate ◽  
Riemannian Manifolds ◽  
Wave Equations ◽  
Energy Decay ◽  
Critical Potential ◽  
Energy Decay Rate

scholarly journals Energy Decay Rate of Wave Equations with Indefinite Damping

2000 ◽  
Vol 161 (2) ◽  
pp. 337-357 ◽  
Author(s):  
Ahmed Benaddi ◽  
Bopeng Rao
Keyword(s):  
Decay Rate ◽  
Wave Equations ◽  
Energy Decay ◽  
Energy Decay Rate

scholarly journals Energy decay rate for a quasi-linear wave equation with localized strong dissipation

2011 ◽  
Vol 62 (1) ◽  
pp. 164-172 ◽  
Author(s):  
Daewook Kim ◽  
Yong Han Kang ◽  
Mi Jin Lee ◽  
Il Hyo Jung
Keyword(s):  
Wave Equation ◽  
Decay Rate ◽  
Energy Decay ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Energy Decay Rate

scholarly journals A Note on Stokes Approximations to Leray Solutions of the Incompressible Navier–Stokes Equations in ℝn

Fluids ◽  
2021 ◽  
Vol 6 (10) ◽  
pp. 340
Author(s):  
Joyce Rigelo ◽  
Janaína Zingano ◽  
Paulo Zingano
Keyword(s):  
Decay Rate ◽  
Stokes Flow ◽  
Stokes Equations ◽  
Energy Decay ◽  
Energy Norm ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Energy Decay Rate ◽  
The Difference

In the early 1980s it was well established that Leray solutions of the unforced Navier–Stokes equations in Rn decay in energy norm for large t. With the works of T. Miyakawa, M. Schonbek and others it is now known that the energy decay rate cannot in general be any faster than t−(n+2)/4 and is typically much slower. In contrast, we show in this note that, given an arbitrary Leray solution u(·,t), the difference of any two Stokes approximations to the Navier–Stokes flow u(·,t) will always decay at least as fast as t−(n+2)/4, no matter how slow the decay of ∥u(·,t)∥L2(Rn) might be.

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