A global unique solvability of entropic weak solution to the one-dimensional pressureless Euler system with a flocking dissipation

Seung-Yeal Ha Feimin Huang Yi Wang

Analysis of PDEs mathscidoc:1912.43756

Journal of Differential Equations, 257, (5), 1333-1371, 2014.9
We present a unique global solvability and flocking estimate of an entropic weak solution to the one-dimensional pressureless Euler system with a flocking dissipation in all-to-all coupling setting. This model appears naturally as a quasi-equilibrium model for hydrodynamic description of CuckerSmale flocking. For the unique global solvability, we adopt the variation approach from Ding and Huang's work [19] on the inhomogeneous pressureless gas dynamic model. When initial mass and velocity are locally integrable and bounded measurable functions, respectively, we give explicit representations for the global entropic weak solutions. Our results do not require any smallness of initial data except that initial mass density is almost everywhere positive.
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@inproceedings{seung-yeal2014a,
  title={A global unique solvability of entropic weak solution to the one-dimensional pressureless Euler system with a flocking dissipation},
  author={Seung-Yeal Ha, Feimin Huang, and Yi Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205541304640320},
  booktitle={Journal of Differential Equations},
  volume={257},
  number={5},
  pages={1333-1371},
  year={2014},
}
Seung-Yeal Ha, Feimin Huang, and Yi Wang. A global unique solvability of entropic weak solution to the one-dimensional pressureless Euler system with a flocking dissipation. 2014. Vol. 257. In Journal of Differential Equations. pp.1333-1371. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205541304640320.
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