Low regularity local well-posedness of the Derivative Nonlinear Schrödinger Equation with periodic initial data

Details Low regularity local well-posedness of the Derivative Nonlinear Schrödinger Equation with periodic initial data Low regularity local well-posedness of the Derivative Nonlinear Schrödinger Equation with periodic initial data

2007-04-23

arxiv.org/abs/0704.2996v1

SIAM J. Math. Anal. (2008), Vol. 39, No. 6, pp. 1890-1920

Mathematics

Analysis of PDEs

29 pages, 1 figure

Scientific paper

10.1137/070689139

The Cauchy problem for the derivative nonlinear Schr\"odinger equation with periodic boundary condition is considered. Local well-posedness for periodic initial data u_0 in the space ^H^s_r, defined by the norms ||u_0||_{^H^s_r}=||^s ^u_0||_{l^r'} is shown in the parameter range s>= 1/2, 2>r>4/3. The proof is based on an adaptation of the gauge transform to the periodic setting and an appropriate variant of the Fourier restriction norm method.

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