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Anisotropically weighted Lq$L^q$‐Lr$L^r$ estimates of the Oseen semigroup in exterior domains, with applications to the Navier–Stokes flow past a rigid body

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  • Tomoki Takahashi

Abstract

We consider the spatial–temporal behavior of the Navier–Stokes flow past a rigid body in R3$\mathbb {R}^3$. This paper develops analysis in Lebesgue spaces with anisotropic weights (1+|x|)α(1+|x|−x1)β${(1+|x|)}^\alpha {(1+|x|-x_1)}^\beta$, which naturally arise in the asymptotic structure of fluid when the translational velocity of the body is parallel to the x1‐direction. We derive anisotropically weighted Lq$L^q$‐Lr$L^r$ estimates for the Oseen semigroup in exterior domains. As applications of those estimates, we study the stability/attainability of the Navier–Stokes flow in anisotropically weighted Lq$L^q$ spaces to get the spatial–temporal behavior of nonstationary solutions.

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  • Tomoki Takahashi, 2024. "Anisotropically weighted Lq$L^q$‐Lr$L^r$ estimates of the Oseen semigroup in exterior domains, with applications to the Navier–Stokes flow past a rigid body," Mathematische Nachrichten, Wiley Blackwell, vol. 297(1), pages 302-354, January.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:1:p:302-354
    DOI: 10.1002/mana.202200419
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    References listed on IDEAS

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    1. Toshiaki Hishida, 2021. "An alternative proof of $$L^q$$ L q – $$L^r$$ L r estimates of the Oseen semigroup in higher dimensional exterior domains," Partial Differential Equations and Applications, Springer, vol. 2(2), pages 1-12, April.
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