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arXiv · 1109.3527

Local well-posedness for the Zakharov system on multidimensional torus

Nobu Kishimoto
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Abstract

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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Nobu Kishimoto. 2011-09-16. Local well-posedness for the Zakharov system on multidimensional torus. https://arxiv.org/abs/1109.3527

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