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Nonlinear artificial boundary conditions with pointwise error estimates for the exterior three dimensional Navier–Stokes problem
Author(s) -
Nazarov Sergej A.,
Specovius–Neugebauer Maria
Publication year - 2003
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.200310039
Subject(s) - mathematics , pointwise , uniqueness , domain (mathematical analysis) , ball (mathematics) , mathematical analysis , truncation (statistics) , nonlinear system , dirichlet boundary condition , boundary (topology) , dirichlet problem , boundary value problem , intersection (aeronautics) , statistics , physics , quantum mechanics , engineering , aerospace engineering
On a three–dimensional exterior domain Ω we consider the Dirichlet problem for the stationary Navier–Stokes system. We construct an approximation problem on the domain Ω R , which is the intersection of Ω with a sufficiently large ball, while we create nonlinear, but local artificial boundary conditions on the truncation boundary. We prove existence and uniqueness of the solutions to the approximating problem together with asymptotically precise pointwise error estimates as R tends to infinity.