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

Tomoki Takahashi

Mathematische Nachrichten, 2024, vol. 297, issue 1, 302-354

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.

Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202200419

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:297:y:2024:i:1:p:302-354

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().