Advanced Studies in Pure Mathematics

Weighted estimate of Stokes semigroup in unbounded domains

Takayuki Kobayashi and Takayuki Kubo

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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

Source
Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 427-435

Dates
Received: 13 December 2011
Revised: 16 February 2012
First available in Project Euclid: 30 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1540934240

Digital Object Identifier
doi:10.2969/aspm/06410427

Mathematical Reviews number (MathSciNet)
MR3381309

Zentralblatt MATH identifier
1335.35183

Subjects
Primary: 35K45: Initial value problems for second-order parabolic systems 76D05: Navier-Stokes equations [See also 35Q30]

Keywords
Weighted estimates $L^p - L^q$ estimate of Stokes semigroup exterior domain perturbed half-space Navier–Stokes equations

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


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