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L q ‐estimates for the stationary Oseen equations on the exterior of a rotating obstacle
Author(s) -
Kim Dugyu
Publication year - 2018
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.4911
Subject(s) - mathematics , sobolev space , uniqueness , mathematical analysis , domain (mathematical analysis) , weak solution , duality (order theory) , space (punctuation) , dirichlet problem , mathematical physics , pure mathematics , boundary value problem , philosophy , linguistics
We study the Dirichlet problem for the stationary Oseen equations around a rotating body in an exterior domain. Our main results are the existence and uniqueness of weak and very weak solutions satisfying appropriate L q ‐estimates. The uniqueness of very weak solutions is shown by the method of cut‐off functions with an anisotropic decay. Then our existence result for very weak solutions is deduced by a duality argument from the existence and estimates of strong solutions. From this and interior regularity of very weak solutions, we finally establish the complete D 1, r ‐result for weak solutions of the Oseen equations around a rotating body in an exterior domain, where 4/3< r <4. Here, D 1, r is the homogeneous Sobolev space.