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arXiv · 1205.5205

Periodic Cubic Hyperbolic Schrödinger equation on $\T^2$

Yuzhao Wang
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Abstract

We consider the cubic Hyperbolic Schrödinger equation \eqref{eq:nls} on torus $\T^2$. We prove that sharp $L^4$ Strichartz estimate, which implies that \eqref{eq:nls} is analytic locally well-posed in in $H^s(\T^2)$ with $s>1/2$, meanwhile, the ill-posedness in $H^s(\T^2)$ for $s<1/2$ is also obtained. The main difficulty comes from estimating the number of representations of an integer as a difference of squares.

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Yuzhao Wang. 2013-04-21. Periodic Cubic Hyperbolic Schrödinger equation on $\T^2$. https://arxiv.org/abs/1205.5205

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