On the Cauchy problem for the derivative nonlinear Schroedinger equation with periodic boundary condition

Details On the Cauchy problem for the derivative nonlinear Schroedinger equation with periodic boundary condition On the Cauchy problem for the derivative nonlinear Schroedinger equation with periodic boundary condition

2005-12-20

arxiv.org/abs/math/0512461v1

Int. Math. Res. Not., Volume 2006, Article ID 96763, 2006

Mathematics

Analysis of PDEs

22 pages

Scientific paper

It is shown that the Cauchy problem for the DNLS equation in the spatially
periodic setting is locally well-posed in Sobolev spaces H^s(T) for s \geq 1/2.
Moreover, global well-posedness is shown for s \geq 1 and data with small L^2
norm.

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