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arXiv · 1309.4336

Well-posedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data

Hiroyuki Hirayama
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Abstract

In the present paper, we consider the Cauchy problem of a system of quadratic derivative nonlinear Schrödinger equations which was introduced by M. Colin and T. Colin (2004) as a model of laser-plasma interaction. The local existence of the solution of the system in the Sobolev space $H^{s}$ for $s>d/2+3$ is proved by M. Colin and T. Colin. We prove the well-posedness of the system with low regularity initial data. For some cases, we also prove the well-posedness and the scattering at the scaling critical regularity by using $U^{2}$ space and $V^{2}$ space which are applied to prove the well-posedness and the scattering for KP-II equation at the scaling critical regularity by Hadac, Herr and Koch (2009).

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Hiroyuki Hirayama. 2013-11-07. Well-posedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data. https://doi.org/10.3934/cpaa.2014.13.1563

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