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Navier-Stokes equations for elliptic complexes

  • We continue our study of invariant forms of the classical equations of mathematical physics, such as the Maxwell equations or the Lamé system, on manifold with boundary. To this end we interpret them in terms of the de Rham complex at a certain step. On using the structure of the complex we get an insight to predict a degeneracy deeply encoded in the equations. In the present paper we develop an invariant approach to the classical Navier-Stokes equations.

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Author:Azal Mera, Alexander ShlapunovORCiDGND, Nikolai Nikolaevich TarkhanovORCiDGND
ISSN:2193-6943 (online)
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (4 (2015)12)
Publisher:Universitätsverlag Potsdam
Place of publication:Potsdam
Document Type:Preprint
Year of first Publication:2015
Year of Completion:2015
Publishing Institution:Universität Potsdam
Publishing Institution:Universitätsverlag Potsdam
Release Date:2015/12/21
Tag:Navier-Stokes equations; classical solution
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Kxx Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] / 35K55 Nonlinear parabolic equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q30 Navier-Stokes equations [See also 76D05, 76D07, 76N10]
76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX) / 76Dxx Incompressible viscous fluids / 76D05 Navier-Stokes equations [See also 35Q30]
Collections:Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2015
Publication Way:Universitätsverlag Potsdam
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht