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This paper provides a small data global existence result for a class ofquadratic derivative nonlinear Schr\"odinger systems in two space dimensions.This is an extension of the previous results by Li [Discrete Contin. Dyn.Syst., 32 (2012), 4265--4285] and Ikeda--Katayama--Sunagawa [Ann. H. Poincar\'e16 (2015), 535--567].

Small data global existence for a class of quadratic derivative nonlinear Schr\"odinger systems in two space dimensions