Weighted estimate of Stokes semigroup in unbounded domains

Abstract

We show $L^p - L^q$ estimates with the $\langle x\rangle^s$ type weight of Stokes semigroup in exterior domains and perturbed half-spaces. Moreover as application of these estimates, we obtain weighted estimates for global solution to the Navier–Stokes equations with small data in these domains.

Article information

Dates
Revised: 16 February 2012
First available in Project Euclid: 30 October 2018

https://projecteuclid.org/ euclid.aspm/1540934240

Digital Object Identifier
doi:10.2969/aspm/06410427

Mathematical Reviews number (MathSciNet)
MR3381309

Zentralblatt MATH identifier
1335.35183

Citation

Kobayashi, Takayuki; Kubo, Takayuki. Weighted estimate of Stokes semigroup in unbounded domains. Nonlinear Dynamics in Partial Differential Equations, 427--435, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06410427. https://projecteuclid.org/euclid.aspm/1540934240