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On the Navier–Stokes equations with free convection in three‐dimensional unbounded triangular channels
Author(s) -
Constales D.,
Kraußhar R. S.
Publication year - 2008
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.941
Subject(s) - mathematics , projector , holomorphic function , kernel (algebra) , domain (mathematical analysis) , bergman kernel , block (permutation group theory) , mathematical analysis , operator (biology) , navier–stokes equations , pure mathematics , geometry , compressibility , biochemistry , chemistry , repressor , computer science , transcription factor , computer vision , gene , engineering , aerospace engineering
The quaternionic calculus is a powerful tool for treating the Navier–Stokes equations very elegantly and in a compact form, through the evaluation of two types of integral operators: the Teodorescu operator and the quaternionic Bergman projector. While the integral kernel of the Teodorescu transform is universal for all domains, the kernel function of the Bergman projector, called the Bergman kernel, depends on the geometry of the domain. In this paper, we use special variants of quaternionic‐holomorphic multiperiodic functions in order to obtain explicit formulas for unbounded three‐dimensional parallel plate channels, rectangular block domains and regular triangular channels. Copyright © 2007 John Wiley & Sons, Ltd.