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arXiv · 2505.06681

Local well-posedness for a system of quadratic derivative nonlinear Schr\"{o}dinger equations

Kohei Akase
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Abstract

We consider the Cauchy problem for a system of quadratic derivative nonlinear Schr\"odinger equations introduced by M. Colin and T. Colin (2004) as a model of laser-plasma interaction. Under the condition that the flow map fails to be twice differentiable, Hirayama, Kinoshita, and Okamoto (2022) proved the well-posedness by constructing a modified energy and applying the energy method. In the present paper, we improve the well-posedness result under the above condition by using the short-time Fourier restriction norm method.

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Kohei Akase. 2025-05-10. Local well-posedness for a system of quadratic derivative nonlinear Schr\"{o}dinger equations. https://arxiv.org/abs/2505.06681

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