TY - CONF
A1 - Constales, Denis
A1 - Kraußhar, Rolf Sören
A2 - Gürlebeck, Klaus
A2 - Könke, Carsten
T1 - ON THE NAVIER-STOKES EQUATION WITH FREE CONVECTION IN STRIP DOMAINS AND 3D TRIANGULAR CHANNELS
N2 - The Navier-Stokes equations and related ones can be treated very elegantly with the quaternionic operator calculus developed in a series of works by K. Guerlebeck, W. Sproeossig and others. This study will be extended in this paper. In order to apply the quaternionic operator calculus to solve these types of boundary value problems fully explicitly, one basically needs to evaluate 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. With special variants of quaternionic holomorphic multiperiodic functions we obtain explicit formulas for three dimensional parallel plate channels, rectangular block domains and regular triangular channels. The explicit knowledge of the integral kernels makes it then possible to evaluate the operator equations in order to determine the solutions of the boundary value problem explicitly.
KW - Architektur
KW - CAD
KW - Computerunterstütztes Verfahren
Y1 - 2006
UR - https://e-pub.uni-weimar.de/opus4/frontdoor/index/index/docId/2938
UR - https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170327-29387
UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER -