Large data local solutions for the derivative NLS equation
  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 $n \geq 2$. 
Ioan Bejenaru, Daniel Tataru