scholarly journals A decay estimate for the eigenvalues of the Neumann-Poincaré operator using the Grunsky coefficients

2019 ◽  
Vol 148 (2) ◽  
pp. 591-600 ◽  
Author(s):  
YoungHoon Jung ◽  
Mikyoung Lim
Keyword(s):  
Decay Estimate ◽  
Grunsky Coefficients

Optimal L 2 -decay of solutions to a cubic dissipative nonlinear Schrödinger equation

2021 ◽  
pp. 1-13
Author(s):  
Kita Naoyasu ◽  
Sato Takuya
Keyword(s):  
Sobolev Space ◽  
Global Solution ◽  
Initial Value Problem ◽  
Trivial Solution ◽  
Decay Estimate ◽  
Weighted Sobolev Space ◽  
The Other ◽  
Initial Value ◽  
Decay Of Solutions ◽  
Dissipative Nonlinearity

This paper presents the optimality of decay estimate of solutions to the initial value problem of 1D Schrödinger equations containing a long-range dissipative nonlinearity, i.e., λ | u | 2 u. Our aim is to obtain the two results. One asserts that, if the L 2 -norm of a global solution, with an initial datum in the weighted Sobolev space, decays at the rate more rapid than ( log t ) − 1 / 2 , then it must be a trivial solution. The other asserts that there exists a solution decaying just at the rate of ( log t ) − 1 / 2 in L 2 .

Global existence and time decay estimate of solutions to the Keller–Segel system

2018 ◽  
Vol 42 (1) ◽  
pp. 375-402
Author(s):  
Zhong Tan ◽  
Jianfeng Zhou
Keyword(s):  
Global Existence ◽  
Decay Estimate ◽  
Time Decay

scholarly journals Time Decay Estimate with Diffusion Wave Property and Smoothing Effect for Solutions to the Compressible Navier-Stokes-Korteweg System

2021 ◽  
Vol 64 (2) ◽  
pp. 163-187
Author(s):  
Takayuki Kobayashi ◽  
Kazuyuki Tsuda
Keyword(s):  
Decay Estimate ◽  
Navier Stokes ◽  
Smoothing Effect ◽  
Time Decay ◽  
Diffusion Wave ◽  
Wave Property

Exact decay estimate on solutions of critical p-Laplacian equations in R+N

2019 ◽  
Vol 469 (1) ◽  
pp. 220-238
Author(s):  
Xiangqing Liu ◽  
Junfang Zhao ◽  
Jiaquan Liu
Keyword(s):  
Decay Estimate ◽  
Laplacian Equations

DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH MEMORY-TYPE DISSIPATION

2012 ◽  
Vol 22 (02) ◽  
pp. 1150012 ◽  
Author(s):  
YONGQIN LIU ◽  
SHUICHI KAWASHIMA
Keyword(s):  
Decay Estimate ◽  
Pointwise Estimate ◽  
Decay Property ◽  
Memory Term ◽  
Fourier Space ◽  
Initial Value ◽  
Timoshenko System ◽  
Frictional Dissipation ◽  
Memory Type ◽  
With Memory

In this paper we consider the initial value problem for the Timoshenko system with a memory term. We construct the fundamental solution by using the Fourier–Laplace transform and obtain the solution formula of the problem. Moreover, applying the energy method in the Fourier space, we derive the pointwise estimate of solutions in the Fourier space, which gives a sharp decay estimate of solutions. It is shown that the decay property of the system is of the regularity-loss type and is weaker than that of the Timoshenko system with a frictional dissipation.

Long-wave decay due to convective turbulence

1976 ◽  
Vol 73 (3) ◽  
pp. 427-444 ◽  
Author(s):  
Theodore Green ◽  
See Whan Kang
Keyword(s):  
Simple Model ◽  
Rayleigh Number ◽  
Reynolds Stress ◽  
Decay Estimate ◽  
Oscillating Flow ◽  
Convective Turbulence ◽  
Decay Component ◽  
Wave Decay ◽  
Long Wave ◽  
Rectangular Basin

Long waves are generated in a laboratory-size rectangular basin, which is heated uniformly from below. Their subsequent decay is measured, and the decay component due to the action of convective turbulence isolated, using a combination of existing theories and interpretation techniques. An expression is proposed for the turbulent decay decrement as a function of the bulk Rayleigh number. The results agree as well as can be expected with a simple model based on a Reynolds-stress decay estimate obtained by superposing convective thermals on the oscillating flow associated with the long wave.

ON LOCAL ENERGY DECAY ESTIMATE OF THE OSEEN SEMIGROUP IN TWO DIMENSIONS AND ITS APPLICATION

2019 ◽  
pp. 1-33 ◽  
Author(s):  
Yasunori Maekawa
Keyword(s):  
Exterior Domain ◽  
Decay Estimate ◽  
Two Dimensions ◽  
Energy Decay ◽  
Local Energy ◽  
Two Dimensional ◽  
Translation Speed ◽  
Temporal Decay ◽  
Oseen Semigroup

We study the temporal decay estimate of the Oseen semigroup in a two-dimensional exterior domain. We establish the local energy decay estimate with a suitable dependence on the small translation speed, which is a significant improvement of Hishida’s result in 2016. As an application, we prove the $L^{q}$ - $L^{r}$ estimates of the Oseen semigroup uniformly in the small translation speed.

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