naa a22 4500 510781462 CHVBK 20180411083249.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1007/s11854-013-0007-0 doi (NATIONALLICENCE)springer-10.1007/s11854-013-0007-0 Kishimoto Nobu Department of Mathematics, Kyoto University, Sakyo-Ku, Kyoto, Japan aut Local well-posedness for the Zakharov system on the multidimensional torus [Elektronische Daten] [Nobu Kishimoto] The initial value problem of the Zakharov system on the two dimensional torus with general period is shown to be locally well posed in the Sobolev spaces of optimal regularity, including the energy space. Unlike the one dimensional case studied by Takaoka [18], the optimal regularity does not depend on the period of torus. The proof relies on a standard iteration argument using the Bourgain norms. The same strategy is also applicable to three and higher dimensional cases. Hebrew University Magnes Press, 2013 Journal d'Analyse Mathématique The Hebrew University Magnes Press 119/1(2013-04-01), 213-253 0021-7670 119:1<213 2013 119 11854 https://doi.org/10.1007/s11854-013-0007-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0007-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kishimoto Nobu Department of Mathematics, Kyoto University, Sakyo-Ku, Kyoto, Japan aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique The Hebrew University Magnes Press 119/1(2013-04-01), 213-253 0021-7670 119:1<213 2013 119 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer