Optimal weighted estimates of the flows in exterior domains

Bae, Hyeong–Ohk; Roh, Jaiok

doi:10.1016/j.na.2010.04.067

Cited by 16 publications

(4 citation statements)

References 17 publications

(25 reference statements)

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“…There is an extensive literature dealing with decay properties of weak and strong solutions to (1.1) (see, e.g., [1][2][3][5][6][7]10,11,13,15,16,22,[27][28][29]31] and the references therein). It is known that if a ∈ L 3 σ (Ω) of L 3 solenoidal vector fields and if a L 3 (Ω) is sufficiently small, then (1.1) admits a unique strong solution u defined for all t > 0.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Decay rates for the incompressible Navier–Stokes flows in 3D exterior domains

Han

2012

Journal of Functional Analysis

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The exterior nonstationary problem is studied for the 3D Navier-Stokes equations, for which the associated total net force to the boundary may not vanish. The time-decay properties of the strong solution including the first and second derivatives are shown in L q and weighted spaces. In particular, the relation of (weighted) L 1 -summability for smooth solutions is discussed in details between the time decay and the total net force exerted by the fluid to the body. The conclusions in this article improve and extend results in: [H. Bae, B. Jin, Asymptotic behavior for the Navier-Stokes equations in 2D exterior domains, J. Funct. Anal. 240 (2006) 508-529; H. Bae, B. Jin, Temporal and spatial decay rates of Navier-Stokes solutions in exterior domains, Bull. Korean Math. Soc. 44 (2007) 547-567] and in: [C. He, T. Miyakawa, On L 1 -summability and asymptotic profiles for smooth solutions to Navier-Stokes equations in a 3D exterior domain, Math. Z. 245 (2003) 387-417; C. He, T. Miyakawa, On weighted-norm estimates for nonstationary incompressible Navier-Stokes flows in a 3D exterior domain, J. Differential Equations 246 (2009) 2355-2386], respectively.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Decay rates for the incompressible Navier–Stokes flows in 3D exterior domains

Han

2012

Journal of Functional Analysis

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“…(ii) n is called a perturbed half-space if there exists R > 0 such that (2) In what follows, let n be an exterior domain or a perturbed halfspace with smooth boundary. We next introduce the known results on the weighted Lq space.…”

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confidence: 99%

“…(P-NS) and so on. In [2], they considered exterior domains !1 c JRn(n = 2, 3) case and they proved the following asymptotic behavieor as t ---+ oo: if a E L~ n Lr for 1 < r < n and lxl"'a E Lr for 0 < a < n for nr / ( n -ra) < p. Advantage of our results is to have the decay rate without a/2 in the weighted asymptotic behavior as t---+ oo. §3.…”

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Weighted estimate of Stokes semigroup in unbounded domains

Kobayashi¹,

Kubo²

Advanced Studies in Pure Mathematics

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We show LP -Lq estimates with the (x) 8 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 N avier-Stokes equations with small data in these domains. §1. IntroductionLet n c ~n(n 2: 2) be an exterior domain or a perturbed halfspace with smooth boundary. We consider the following Navier-Stokes equations in these unbounded domains n c ~n:

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Pointwise Spatial Decay of Weak Solutions to the Navier–Stokes System in 3D Exterior Domains

Deuring

2015

J. Math. Fluid Mech.

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Optimal weighted estimates of the flows in exterior domains

Cited by 16 publications

References 17 publications

Decay rates for the incompressible Navier–Stokes flows in 3D exterior domains

Decay rates for the incompressible Navier–Stokes flows in 3D exterior domains

Weighted estimate of Stokes semigroup in unbounded domains

Pointwise Spatial Decay of Weak Solutions to the Navier–Stokes System in 3D Exterior Domains

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