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.

Lp-estimates for the wave equation with time-dependent dissipation

2005 ◽  
Vol 135 (2) ◽  
pp. 393-412
Author(s):  
Tokio Matsuyama
Keyword(s):  
Wave Equation ◽  
Exterior Domain ◽  
Wave Speed ◽  
Energy Decay ◽  
Time Dependent ◽  
Local Energy ◽  
Lp Estimates ◽  
Dissipative Wave Equation ◽  
Scattering Rates

We are interested in Lp-estimates and scattering rates for the dissipative wave equation with time-dependent coefficients in an exterior domain outside a star-shaped obstacle. We want to notice the case that the support of dissipation expands strictly less than the wave speed. We develop a new cut-off method, which is time dependent. For this, we shall obtain the local energy decay over the time-dependent subdomain

On a local energy decay estimate of solutions to the hyperbolic type Stokes equations

2018 ◽  
Vol 264 (10) ◽  
pp. 6061-6081
Author(s):  
Takayuki Kobayashi ◽  
Takayuki Kubo ◽  
Kenji Nakamura
Keyword(s):  
Decay Estimate ◽  
Stokes Equations ◽  
Energy Decay ◽  
Hyperbolic Type ◽  
Local Energy

Urbanicity, City Delegations, and Two-Dimensional Liberalism

2018 ◽  
Author(s):  
Thomas K. Ogorzalek
Keyword(s):  
National Level ◽  
Two Dimensions ◽  
Political Order ◽  
Two Dimensional ◽  
Local Institutions ◽  
Horizontal Integration ◽  
National Politics ◽  
United Front ◽  
Strategies For Success

This theoretical chapter develops the argument that the conditions of cities—large, densely populated, heterogeneous communities—generate distinctive governance demands supporting (1) market interventions and (2) group pluralism. Together, these positions constitute the two dimensions of progressive liberalism. Because of the nature of federalism, such policies are often best pursued at higher levels of government, which means that cities must present a united front in support of city-friendly politics. Such unity is far from assured on the national level, however, because of deep divisions between and within cities that undermine cohesive representation. Strategies for success are enhanced by local institutions of horizontal integration developed to address the governance demands of urbanicity, the effects of which are felt both locally and nationally in the development of cohesive city delegations and a unified urban political order capable of contending with other interests and geographical constituencies in national politics.

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