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arXiv · 1312.5249

Existence and Uniqueness theory for the fractional Schrödinger equation on the torus

S. Demirbas·M. B. Erdoğan·N. Tzirakis
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Abstract

We study the Cauchy problem for the $1$-d periodic fractional Schrödinger equation with cubic nonlinearity. In particular we prove local well-posedness in Sobolev spaces, for solutions evolving from rough initial data. In addition we show the existence of global-in-time infinite energy solutions. Our tools include a new Strichartz estimate on the torus along with ideas that Bourgain developed in studying the periodic cubic NLS.

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S. Demirbas, M. B. Erdoğan, N. Tzirakis. 2013-12-18. Existence and Uniqueness theory for the fractional Schrödinger equation on the torus. https://arxiv.org/abs/1312.5249

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