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 Local well-posedness of Dirac equations with nonlinearity derived from honeycomb structure in 2 dimensions Bull. Korean Math. Soc.Published online September 10, 2021 Kiyeon Lee Ewha Womans University Abstract : The aim of this paper is to show local well-posedness of 2 dimensional Dirac equations with honeycomb lattice nonlinearity and Hartree type nonlinearity in $H^s$ for $s>\frac38$ and $s>\frac78$, respectively. To this end, we use a bilinear estimate derived from Selberg's argument(\cite{sel}). We also provide the smoothness failure of flows of Dirac equations. Keywords : Dirac equations, Honeycomb lattice, local well-posedness, non-smoothness, Bourgain's space. MSC numbers : 35Q55, 35Q40 Full-Text :