Local well-posedness for the Zakharov system on multidimensional torus

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

2011-09-16

arxiv.org/abs/1109.3527v1

Mathematics

Analysis of PDEs

35 pages, 3 figures

Scientific paper

The initial value problem of the Zakharov system on two dimensional torus
with general period is shown to be locally well-posed in the Sobolev spaces of
optimal regularity, including the energy space. Proof relies on a standard
iteration argument using the Bourgain norms. The same strategy is also
applicable to three and higher dimensional cases.

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