# Bulletin of theKorean Mathematical SocietyBKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

## Article

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Bull. Korean Math. Soc. 2021; 58(6): 1445-1461

Published online November 30, 2021 https://doi.org/10.4134/BKMS.b201040

## Local well-posedness of Dirac equations with nonlinearity derived from honeycomb structure in 2 dimensions

Kiyeon Lee

Ewha Womans University

### Abstract

The aim of this paper is to show the local well-posedness of 2 dimensional Dirac equations with power type and Hartree type nonlinearity derived from honeycomb structure in $H^s$ for $s>\frac78$ and $s>\frac38$, respectively. 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: Primary 35Q55, 35Q40

Supported by: http://bkms.kms.or.kr/journal/view.html?doi=10.4134/BKMS.b201040