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

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.

preprint2013arXivOpen access
S. DemirbasM. B. ErdoğanN. Tzirakis
math.AP
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Open access3 authors1 topic
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
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S. DemirbasM. B. ErdoğanN. Tzirakis

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