Well-posedness for a system of quadratic derivative nonlinear Schr\"odinger equations in almost critical spaces

Hiroyuki Hirayama; Mamoru Okamoto; Shinya Kinoshita

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arxiv 2009.13072 v1 pith:WWERFUXU submitted 2020-09-25 math.AP

Well-posedness for a system of quadratic derivative nonlinear Schr\"odinger equations in almost critical spaces

Hiroyuki Hirayama , Shinya Kinoshita , Mamoru Okamoto This is my paper

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keywords almostcauchycolincriticalderivativeequationsnonlinearodinger

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In this paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schr\"odinger equations introduced by Colin and Colin (2004). We determine an almost optimal Sobolev regularity where the smooth flow map of the Cauchy problem exists, expect for the scaling critical case. This result covers a gap left open in papers of the first and second authors (2014, 2019).

Well-posedness for a system of quadratic derivative nonlinear Schr\"odinger equations in almost critical spaces

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