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Besov regularity for the Stokes and the Navier‐Stokes system in polyhedral domains
Author(s) -
Eckhardt F.
Publication year - 2015
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201300096
Subject(s) - besov space , sobolev space , mathematical proof , mathematics , wavelet , nonlinear system , scale (ratio) , navier–stokes equations , mathematical analysis , pure mathematics , computer science , interpolation space , geometry , physics , compressibility , artificial intelligence , biochemistry , chemistry , functional analysis , quantum mechanics , gene , thermodynamics
In this paper we study the regularity of solutions to the Stokes and the Navier‐Stokes system in polyhedral domains contained in ℝ 3 . We consider the scale B s τ (L τ ), 1/τ = s/3 + 1/2 of Besov spaces which determines the approximation order of adaptive numerical wavelet schemes and other nonlinear approximation methods. We show that the regularity in this scale is large enough to justify the use of adaptive methods. The proofs of the main results are performed by combining regularity results in weighted Sobolev spaces with characterizations of Besov spaces by wavelet expansions.