Anisotropically weighted \(L^q-L^r\) estimates of the Oseen semigroup in exterior domains, with applications to the Navier-Stokes flow past a rigid body. (English) Zbl 1531.35230
Summary: We consider the spatial-temporal behavior of the Navier-Stokes flow past a rigid body in \(\mathbb{R}^3\). This paper develops analysis in Lebesgue spaces with anisotropic weights \({(1+|x|)}^\alpha {(1+|x|-x_1)}^\beta\), which naturally arise in the asymptotic structure of fluid when the translational velocity of the body is parallel to the \(x_1\)-direction. We derive anisotropically weighted \(L^q-L^r\) 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 \(L^q\) spaces to get the spatial-temporal behavior of nonstationary solutions.
© 2023 Wiley-VCH GmbH.
© 2023 Wiley-VCH GmbH.
MSC:
| 35Q30 | Navier-Stokes equations |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
Keywords:
anisotropically weighted \(L^q\) space; attainability; Navier-Stokes flow; Oseen flow; stability; starting problemReferences:
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