Journal d'Analyse Mathématique

, Volume 119, Issue 1, pp 213–253 | Cite as

Local well-posedness for the Zakharov system on the multidimensional torus

  • Nobu KishimotoEmail author


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.


High Dimensional Case Optimal Regularity Bilinear Estimate Zakharov Equation ZAKHAROV System 
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© Hebrew University Magnes Press 2013

Authors and Affiliations

  1. 1.Department of MathematicsKyoto UniversitySakyo-Ku, KyotoJapan

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