Local well-posedness for the derivative nonlinear Schrödinger equation in Besov spaces

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Abstract: It is shown that the cubic derivative nonlinear Schr"odinger equation is locally well-posed in Besov spaces

B_{2, i n f t y}^{s} (m a t h b b X)

,

s g e f r a c 12

, where we treat the non-periodic setting

m a t h b b X = m a t h b b R

and the periodic setting

m a t h b b X = m a t h b b T

simultaneously. The proof is based on the strategy of Herr for initial data in

H^{s} (m a t h b b T)

,

s g e f r a c 12

.

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