Advanced Studies in Pure Mathematics

Weighted estimate of Stokes semigroup in unbounded domains

Takayuki Kobayashi and Takayuki Kubo

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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

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

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

Permanent link to this document euclid.aspm/1540934240

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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