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Decay Results of Higher-Order Norms for the Navier–Stokes Flows in 3D Exterior Domains

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Abstract

Using the nonstationary Stokes solution formula and the regularity theory of the steady Stokes equations, we establish the decay results (including the weighted cases) of higher-order spatial derivatives for the Navier–Stokes flows in 3D exterior domains, which is a long standing problem. The higher-order norm (weighted) decay results in this article are inspired by the work in Bae and Jin (Proc R Soc Edinburgh Sect A 135:461–477, 2005), Schonbek and Wiegner (Proc R Soc Edinburgh Sect A 126:677–685, 1996), respectively, which are considered in the whole space.

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  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Pigong Han

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  1. Pigong Han
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Correspondence to Pigong Han.

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Communicated by L. Caffarelli

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Han, P. Decay Results of Higher-Order Norms for the Navier–Stokes Flows in 3D Exterior Domains. Commun. Math. Phys. 334, 397–432 (2015). https://doi.org/10.1007/s00220-014-2151-5

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