arXiv subjects

Kohei Akase

Publications and source records attributed to Kohei Akase.

2 recordsLinked to original sources

arXiv2025

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

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.

math.AP↗

arXiv2023

Well-posedness for a nonlinear Schr\"{o}dinger equation with quadratic derivative nonlinearities for bounded primitive initial data

We consider the Cauchy problem for a quadratic derivative nonlinear Schr\"odinger equation whose nonlinearity is a linear combination of $\partial_x (u^2)$ and $\partial_x (|u|^2)$. We prove the local well-posedness in the $L^2$-based Sobolev space $H^s(\mathbb{R})$ for $s\ge 0$ with bounded primitives. Moreover, we prove the global well-posedness in $H^s(\mathbb{R})$ for $s\ge 1$ and a special case of the coefficients of nonlinearities.

math.AP↗