 |
|
|
|
| HAL : hal-00614736, version 1 |
| arXiv : 1108.3160 |
| Fiche détaillée |  Récupérer au format |
|
|
|
|
| Hydrodynamic models of self-organized dynamics: derivation and existence theory |
|
|
| Pierre Degond 1Jian-Guo Liu 2 |
|
|
| (15/08/2011) |
|
|
|
| This paper is concerned with the derivation and analysis of hydrodynamic models for systems of self-propelled particles subject to alignment interaction and attraction-repulsion. The starting point is the kinetic model considered in earlier work of Degond & Motsch with the addition of an attraction-repulsion interaction potential. Introducing different scalings than in Degond & Motsch, the non-local effects of the alignment and attraction-repulsion interactions can be kept in the hydrodynamic limit and result in extra pressure, viscosity terms and capillary force. The systems are shown to be symmetrizable hyperbolic systems with viscosity terms. A local-in-time existence result is proved in the 2D case for the viscous model and in the 3D case for the inviscid model. The proof relies on the energy method. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Institut de Mathématiques de Toulouse (IMT) |
|
|
|
Université Paul Sabatier - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées de Toulouse – CNRS : UMR5219 |
|
|
| 2 : | Duke Physics |
|
|
|
Duke University |
|
|
| 3 : | Department of Mathematics, University of Maryland |
|
|
|
University of Maryland |
|
|
| 4 : | Department of Mathematics, |
|
|
|
California State University Northridge |
|
|
|
|
|
|
|
|
|
| Domaine | : | Mathématiques/Physique mathématique |
|
|
| Liste des fichiers attachés à ce document : | ||||||||||
|
||||||||||
|
|
|
| hal-00614736, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00614736 | |
| oai:hal.archives-ouvertes.fr:hal-00614736 | |
| Contributeur : Pierre Degond | |
| Soumis le : Lundi 15 Août 2011, 23:41:08 | |
| Dernière modification le : Mardi 16 Août 2011, 08:10:24 | |
