Preprint
The Navier-Stokes Equations with Particle Methods
Zusammenfassung
The non-stationary nonlinear Navier-Stokes equations describe the motion of a viscous incompressible fluid flow for 0<t≤T in some bounded three-dimensional domain.
Up to now it is not known wether these equations are well-posed or not. Therefore we use a particle method to develop a system of approximate equations. We show that this system can be solved uniquely and globally in time and that its solution has a high degree of spatial regularity. Moreover we prove that the system of approximate solutions has an accumulation point satisfying the Navier-Stokes equations in a weak sense.
Up to now it is not known wether these equations are well-posed or not. Therefore we use a particle method to develop a system of approximate equations. We show that this system can be solved uniquely and globally in time and that its solution has a high degree of spatial regularity. Moreover we prove that the system of approximate solutions has an accumulation point satisfying the Navier-Stokes equations in a weak sense.
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@article{urn:nbn:de:hebis:34-2008022020404,
author={Varnhorn, Werner},
title={The Navier-Stokes Equations with Particle Methods},
year={2007}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2007$n2007 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-2008022020404 3000 Varnhorn, Werner 4000 The Navier-Stokes Equations with Particle Methods / Varnhorn, Werner 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-2008022020404=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel ;; 07, 04 7136 ##0##urn:nbn:de:hebis:34-2008022020404
2008-02-20T11:03:46Z 2008-02-20T11:03:46Z 2007 urn:nbn:de:hebis:34-2008022020404 http://hdl.handle.net/123456789/2008022020404 301779 bytes application/pdf eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Navier-Stokes approximation weak solutions compatibility condition 510 The Navier-Stokes Equations with Particle Methods Preprint The non-stationary nonlinear Navier-Stokes equations describe the motion of a viscous incompressible fluid flow for 0<t≤T in some bounded three-dimensional domain. Up to now it is not known wether these equations are well-posed or not. Therefore we use a particle method to develop a system of approximate equations. We show that this system can be solved uniquely and globally in time and that its solution has a high degree of spatial regularity. Moreover we prove that the system of approximate solutions has an accumulation point satisfying the Navier-Stokes equations in a weak sense. open access Varnhorn, Werner Mathematische Schriften Kassel ;; 07, 04 35B65 35D05 76D05 Mathematische Schriften Kassel 07, 04
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