Weighted Lp − Lq estimates of Stokes semigroup in exterior domains
نویسندگان
چکیده
We consider the Navier-Stokes equations in exterior domains and in the weighted L space. For this purpose, we consider the L − L estimates of Stokes semigroup with weight 〈x〉 type. Our proof is based on the cut-off technique with local energy decay estimate proved by Dan, Kobayashi and Shibata [1] and the weighted L − L estimates of Stokes semigroup in the whole space proved by Kobayashi and Kubo [2]. Finally, as the application of the weighted L − L estimates to the Navier-Stokes equations, we obtain the weighted asymptotic behavior of global solution as t→∞.
منابع مشابه
The L∞-Stokes semigroup in exterior domains
The Stokes semigroup on a bounded domain is an analytic semigroup on spaces of bounded functions as was recently shown by the authors based on an a priori L∞-estimate for solutions to the linear Stokes equations. In this paper, we extend our approach to exterior domains and prove that the Stokes semigroup is uniquely extendable to an analytic semigroup on spaces of bounded functions.
متن کاملSmall moving rigid body into a viscous incompressible fluid
We consider a single disk moving under the influence of a 2D viscous fluid and we study the asymptotic as the size of the solid tends to zero. If the density of the solid is independent of ε, the energy equality is not sufficient to obtain a uniform estimate for the solid velocity. This will be achieved thanks to the optimal Lp − Lq decay estimates of the semigroup associated to the fluid-rigid...
متن کاملLp-analyticity of Schrödinger semigroups on Riemannian manifolds
We address the problems of extrapolation, analyticity, and Lp-spectral independence for C0-semigroups in the abstract context of metric spaces with exponentially bounded volume. The main application of the abstract result is Lp-analyticity of angle π 2 of Schrödinger semigroups on Riemannian manifolds with Ricci curvature bounded below, under the condition of form smallness of the negative part...
متن کاملL p weighted theory for Navier - Stokes equations in exterior domains
This paper is devoted to some mathematical questions related to the stationary Navier-Stokes problem in three-dimensional exterior domains. Our approach is based on a combination of properties of Oseen problems in R and in exterior domains of R.
متن کاملTitle: on the Stokes Semigroup in Some Non-helmholtz Domains
Title: The fundamental solution of compressible and incompressible fluid flow past a rotating obstacle Abstract: We consider the flow of either an incompressible or a compressible fluid around or past a rotating rigid body in the whole space R 3. Using a global coordinate transform and a linearization the problem reduces to a linear PDE system in a time-independent domain which may admit statio...
متن کامل