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arXiv · 0704.2996

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

A. Grünrock·S. Herr
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Abstract

The Cauchy problem for the derivative nonlinear Schrödinger 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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A. Grünrock, S. Herr. 2007-04-23. Low regularity local well-posedness of the Derivative Nonlinear Schrödinger Equation with periodic initial data. https://doi.org/10.1137/070689139

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