Preprint
The Navier-Stokes Equations with Time Delay
Abstract
In the present paper we use a time delay epsilon > 0 for an energy conserving approximation of the nonlinear term of the non-stationary Navier-Stokes equations. We prove that the corresponding initial value problem (N_epsilon)in smoothly bounded domains G \subseteq R^3 is well-posed. Passing to the limit epsilon \rightarrow 0 we show that the sequence of stabilized solutions has an accumulation point such that it solves the Navier-Stokes problem (N_0) in a weak sense (Hopf).
Citation
@article{urn:nbn:de:hebis:34-2008022120437,
author={Varnhorn, Werner},
title={The Navier-Stokes Equations with Time Delay},
year={2007}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2007$n2007 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-2008022120437 3000 Varnhorn, Werner 4000 The Navier-Stokes Equations with Time Delay / Varnhorn, Werner 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-2008022120437=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel ;; 07, 05 7136 ##0##urn:nbn:de:hebis:34-2008022120437
2008-02-21T14:24:40Z 2008-02-21T14:24:40Z 2007 urn:nbn:de:hebis:34-2008022120437 http://hdl.handle.net/123456789/2008022120437 98585 bytes 185016 bytes application/pdf application/pdf eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Navier-Stokes Equations 510 The Navier-Stokes Equations with Time Delay Preprint In the present paper we use a time delay epsilon > 0 for an energy conserving approximation of the nonlinear term of the non-stationary Navier-Stokes equations. We prove that the corresponding initial value problem (N_epsilon)in smoothly bounded domains G \subseteq R^3 is well-posed. Passing to the limit epsilon \rightarrow 0 we show that the sequence of stabilized solutions has an accumulation point such that it solves the Navier-Stokes problem (N_0) in a weak sense (Hopf). open access Varnhorn, Werner Mathematische Schriften Kassel ;; 07, 05 65M10 76D05 35A35 35D05 35K55 35Q10 Mathematische Schriften Kassel 07, 05
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