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Large data local solutions for the derivative NLS equation

Ioan Bejenaru; Daniel Tataru — 2008

Journal of the European Mathematical Society

We consider the derivative NLS equation with general quadratic nonlinearities. In [2] 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 $n \geq 2$ .

An abstract approximate controllability result and applications to elliptic and parabolic systems with dynamic boundary conditions.

Bejenaru, Ioan; Diaz, Jesus Ildefonso; Vrabie, Ioan I. — 2001

Electronic Journal of Differential Equations (EJDE) [electronic only]

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