Large data local solutions for the derivative NLS equation (Q952511)

Summary: We consider the derivative NLS equation with general quadratic nonlinearities. In [Trans. Am. Math. Soc. 360, No. 11, 5925--5957 (2008; Zbl 1159.35064)] the first author 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 \(n \geq 2\).