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arXiv · 1311.3119

Well-posedness and scattering for nonlinear Schrödinger equations with a derivative nonlinearity at the scaling critical regularity

Hiroyuki Hirayama
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Abstract

In the present paper, we consider the Cauchy problem of nonlinear Schrödinger equations with a derivative nonlinearity which depends only on $\bar{u}$. The well-posedness of the equation at the scaling subcritical regularity was proved by A. Grünrock (2000). We prove the well-posedness of the equation and the scattering for the solution 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. 2013-11-13. Well-posedness and scattering for nonlinear Schrödinger equations with a derivative nonlinearity at the scaling critical regularity. https://doi.org/10.1619/fesi.58.431

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