Well-posedness for a system of quadratic derivative nonlinear Schr\"odinger equations with radial initial data

Hiroyuki Hirayama; Mamoru Okamoto; Shinya Kinoshita

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Well-posedness for a system of quadratic derivative nonlinear Schr\"odinger equations with radial initial data

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arxiv 1811.08324 v1 pith:XBKZML2D submitted 2018-11-19 math.AP

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

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keywords systemradialcolindataderivativeequationsinitialnonlinear

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abstract

In the present paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schr\"odinger equations. This system was introduced by M. Colin and T. Colin (2004). The first and second authors obtained some well-posedness results in the Sobolev space $H^{s}(\mathbb{R}^d)$. We improve these results for conditional radial initial data by rewriting the system radial form.

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