Format:
1 Online-Ressource (101 Seiten, 765 KB)
Content:
The classical Navier-Stokes equations of hydrodynamics are usually written in terms of vector analysis. More promising is the formulation of these equations in the language of differential forms of degree one. In this way the study of Navier-Stokes equations includes the analysis of the de Rham complex. In particular, the Hodge theory for the de Rham complex enables one to eliminate the pressure from the equations. The Navier-Stokes equations constitute a parabolic system with a nonlinear term which makes sense only for one-forms. A simpler model of dynamics of incompressible viscous fluid is given by Burgers' equation. This work is aimed at the study of invariant structure of the Navier-Stokes equations which is closely related to the algebraic structure of the de Rham complex at step 1. To this end we introduce Navier-Stokes equations related to any elliptic quasicomplex of first order differential operators. These equations are quite similar to the classical Navier-Stokes equations including generalised velocity and pressure…
Note:
Dissertation Universität Potsdam, Mathematisch-Naturwissenschaftliche Fakultät 2017
Additional Edition:
Erscheint auch als Druck-Ausgabe Mera, Azal Jaafar Musa The Navier-Stokes equations for elliptic quasicomplexes Potsdam, 2017
Language:
English
Keywords:
Navier-Stokes-Gleichung
;
Hochschulschrift
URN:
urn:nbn:de:kobv:517-opus4-398495
URL:
https://nbn-resolving.org/urn:nbn:de:kobv:517-opus4-398495
URL:
https://d-nb.info/1218402482/34
Author information:
Tarchanov, Nikolaj Nikolaevič 1955-2020
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