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Existence and exponential stability in L r ‐spaces of stationary Navier–Stokes flows with prescribed flux in infinite cylindrical domains
Author(s) -
Ri MyongHwan,
Farwig Reinhard
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.780
Subject(s) - mathematics , semigroup , uniqueness , mathematical analysis , exponential stability , perturbation (astronomy) , exponential function , infinity , mathematical proof , flux (metallurgy) , analytic semigroup , navier–stokes equations , mathematical physics , physics , geometry , compressibility , thermodynamics , materials science , quantum mechanics , nonlinear system , metallurgy
Abstract We prove existence, uniqueness and exponential stability of stationary Navier–Stokes flows with prescribed flux in an unbounded cylinder of ℝ n ,n⩾3, with several exits to infinity provided the total flux and external force are sufficiently small. The proofs are based on analytic semigroup theory, perturbation theory and L r − L q ‐estimates of a perturbation of the Stokes operator in L q ‐spaces. Copyright © 2006 John Wiley & Sons, Ltd.