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Periodic solutions of the Navier–Stokes equations in a perturbed half‐space and an aperture domain
Author(s) -
Kubo Takayuki
Publication year - 2005
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.618
Subject(s) - mathematics , uniqueness , mathematical analysis , domain (mathematical analysis) , semigroup , dimension (graph theory) , navier–stokes equations , space (punctuation) , stokes flow , compressibility , pure mathematics , geometry , flow (mathematics) , linguistics , philosophy , engineering , aerospace engineering
We shall construct a periodic strong solution of the Navier–Stokes equations for some periodic external force in a perturbed half‐space and an aperture domain of the dimension n ⩾3. Our proof is based on L p – L q estimates of the Stokes semigroup. We apply L p – L q estimates to the integral equation which is transformed from the original equation. As a result, we obtain the existence and uniqueness of periodic strong solutions. Copyright © 2005 John Wiley & Sons, Ltd.