Corpus ID: 119308129

The Mean Field Kinetic Equation for a Pedestrian Flow Model: The Global Existence of Weak Solution

@article{Yin2017TheMF,
  title={The Mean Field Kinetic Equation for a Pedestrian Flow Model: The Global Existence of Weak Solution},
  author={Qitao Yin and L. Chen and Simone Gottlich},
  journal={arXiv: Analysis of PDEs},
  year={2017}
}
In this paper we prove the global existence of the weak solution to the mean field kinetic equation derived from the $N$-particle pedestrian Newtonian system. For $L^1\cap L^\infty$ initial data, the solvability of the mean field kinetic equation can be obtained by using uniform estimates and compactness arguments while difficulties arising from the non-local non-linear interaction are tackled appropriately using the Aubin-Lions compact embedding theorem. 
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