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Weighted estimate of Stokes semigroup in unbounded domains. (English) Zbl 1335.35183
Ei, Shin-Ichiro (ed.) et al., Nonlinear dynamics in partial differential equations. Proceedings of the 4th MSJ-SI international conference, Kyushu, Japan, September 12–21, 2011. Tokyo: Mathematical Society of Japan (ISBN 978-4-86497-022-8/hbk). Advanced Studies in Pure Mathematics 64, 427-435 (2015).
Summary: 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.
For the entire collection see [Zbl 1321.35002].
##### MSC:
 35Q30 Navier-Stokes equations 35K45 Initial value problems for second-order parabolic systems 76D05 Navier-Stokes equations for incompressible viscous fluids