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arXiv · 1508.03076

A priori estimates and weak solutions for the derivative nonlinear Schr\"{o}dinger equation on torus below $H^{1/2}$

Hideo Takaoka
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Abstract

We propose a priori estimates for a weak solution to the derivative nonlinear Schr\"odinger equation (DNLS) on torus with small $L^2$-norm datum in low regularity Sobolev spaces. These estimates allow us to show the existence of solutions in $H^s(\mathbb{T})$ with some $s<1/2$ in a relatively weak sense. Furthermore we make some remarks on the error estimates arising from the finite dimensional approximation solutions of DNLS using the Fourier-Lesbesgue type as auxiliary spaces, despite the fact that Nahmod, Oh, Rey-Bullet and Staffilani \cite{nors} have already seen them.

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Hideo Takaoka. 2015-08-12. A priori estimates and weak solutions for the derivative nonlinear Schr\"{o}dinger equation on torus below $H^{1/2}$. https://arxiv.org/abs/1508.03076

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