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Leading term at infinity of steady Navier‐Stokes flow around a rotating obstacle
Author(s) -
Farwig Reinhard,
Hishida Toshiaki
Publication year - 2011
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200910192
Subject(s) - mathematics , domain (mathematical analysis) , vector field , infinity , measure (data warehouse) , boundary (topology) , flow (mathematics) , term (time) , mathematical analysis , compressibility , constant (computer programming) , dirac measure , field (mathematics) , stokes flow , mathematical physics , physics , geometry , pure mathematics , mechanics , dirac equation , quantum mechanics , dirac algebra , database , computer science , dirac spinor , programming language
Consider a viscous incompressible flow around a body in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb R^3$\end{document} rotating with constant angular velocity ω. Using a coordinate system attached to the body, the problem is reduced to a modified Navier‐Stokes system in a fixed exterior domain. This paper addresses the question of the asymptotic behavior of stationary solutions to the new system as | x | → ∞. Under a suitable smallness assumption on the velocity field, u , and the net force on the boundary, N , we prove that the leading term of u is the so‐called Landau solution U , a singular solution of the stationary Navier‐Stokes system in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb R^3$\end{document} with external force k ωδ 0 and decaying as 1/| x |; here \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$k\in \mathbb R$\end{document} is a suitable constant determined by N and δ 0 is the Dirac measure supported in the origin.