Journal of the European Mathematical Society


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Volume 10, Issue 4, 2008, pp. 957–985
DOI: 10.4171/JEMS/136

Large data local solutions for the derivative NLS equation

Ioan Bejenaru[1] and Daniel Tataru[2]

(1) Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, CA 92093-0112, La Jolla, USA
(2) Department of Mathematics, University of California, CA 94720-3840, Berkeley, USA

We consider the Derivative NLS equation with general quadratic nonlinearities. In \cite{be2} the first author has proved a sharp small data local well-posedness result in Sobolev spaces with a decay structure at infinity in dimension $n = 2$. Here we prove a similar result for large initial data in all dimensions $n \geq 2$.

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Bejenaru Ioan, Tataru Daniel: Large data local solutions for the derivative NLS equation. J. Eur. Math. Soc. 10 (2008), 957-985. doi: 10.4171/JEMS/136