JournalsjemsVol. 10 , No. 4DOI 10.4171/jems/136

Large data local solutions for the derivative NLS equation

  • Daniel Tataru

    University of California, Berkeley, USA
  • Ioan Bejenaru

    University of Chicago, United States
Large data local solutions for the derivative NLS equation cover

Abstract

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=2n = 2. Here we prove a similar result for large initial data in all dimensions n2n \geq 2.