Hydrodynamic models of self-organized dynamics: derivation and existence theory

Pierre Degond Institut de Math´ematiques de Toulouse Jian-Guo Liu Duke University Sébastien Motsch University of Maryland Vladislav Panferov California State University, Northridge

Analysis of PDEs mathscidoc:1702.03041

Methods & Applications of Analysis, 20, (2), 089–114, 2013.6
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.
Physics - Fluid Dynamics, Mathematical Physics
[ Download ] [ 2017-02-08 21:32:43 uploaded by jianguo ] [ 701 downloads ] [ 0 comments ]
@inproceedings{pierre2013hydrodynamic,
  title={Hydrodynamic models of self-organized dynamics: derivation and existence theory},
  author={Pierre Degond, Jian-Guo Liu, Sébastien Motsch, and Vladislav Panferov},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208213243174695316},
  booktitle={Methods & Applications of Analysis},
  volume={20},
  number={2},
  pages={089–114},
  year={2013},
}
Pierre Degond, Jian-Guo Liu, Sébastien Motsch, and Vladislav Panferov. Hydrodynamic models of self-organized dynamics: derivation and existence theory. 2013. Vol. 20. In Methods & Applications of Analysis. pp.089–114. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208213243174695316.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved