Preprint
Lagrangian approximations and weak solutions of the Navier-Stokes equations
Zusammenfassung
The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles of the fluid. The method leads to a sequence of uniquely determined approximate solutions with a high degree of regularity containing a convergent subsequence with limit function v such that v is a weak solution of the Navier-Stokes equations.
Zitieren
@article{urn:nbn:de:hebis:34-2007022617254,
author={Varnhorn, Werner},
title={Lagrangian approximations and weak solutions of the Navier-Stokes equations},
year={2007}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2007$n2007 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-2007022617254 3000 Varnhorn, Werner 4000 Lagrangian approximations and weak solutions of the Navier-Stokes equations / Varnhorn, Werner 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-2007022617254=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel ;; 07, 02 7136 ##0##urn:nbn:de:hebis:34-2007022617254
2007-02-26T10:43:20Z 2007-02-26T10:43:20Z 2007 urn:nbn:de:hebis:34-2007022617254 http://hdl.handle.net/123456789/2007022617254 196288 bytes application/pdf eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Navier-Stokes equations Lagrangian representation Weak solutions 510 Lagrangian approximations and weak solutions of the Navier-Stokes equations Preprint The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles of the fluid. The method leads to a sequence of uniquely determined approximate solutions with a high degree of regularity containing a convergent subsequence with limit function v such that v is a weak solution of the Navier-Stokes equations. open access Varnhorn, Werner Mathematische Schriften Kassel ;; 07, 02 35B65 35D05 76D05 Mathematische Schriften Kassel 07, 02
Die folgenden Lizenzbestimmungen sind mit dieser Ressource verbunden: