Global existence for chemotaxis with finite sampling radius

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MODEL HIERARCHIES FOR CELL AGGREGATION BY CHEMOTAXIS (2006, unknown): “We collect four global existence results: For n = 2, if one of the conditions below is satisfied: Subcritical total mass[12]: uc = χ0∇S with χ0 > 0 and M < 8πD0/χ0, or Quorum sensing 1[18]: uc = χ(ρ)∇S and there is a threshold ρ̄ > 0 such that χ(ρ) = 0 for ρ ≥ ρ̄ or, more generally, Quorum sensing 2”
Global Existence for a Kinetic Model of Chemotaxis via Dispersion and Strichartz Estimates (2007, background): “For more results and models involving kinetic equations, see Chalub and Rodrigues (2006), Filbet et al. (2005), Hillen et al. (2007), for hyperbolic models (Dalibard and Perthame, 2006; Dolak and Schmeiser, 2003; Erban and Hwang, 2006; Hwang et al., 2006) and for surveys on the kinetic aspects…”
A user’s guide to PDE models for chemotaxis (2009, methodology): “Notice that in [37] we claimed that v̄ is a plateau for model (M4).”