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arXiv · 1203.6376

Resonant decomposition and the $I$-method for the two-dimensional Zakharov system

Nobu Kishimoto
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Abstract

The initial value problem of the Zakharov system on two-dimensional torus with general period is considered in this paper. We apply the $I$-method with some 'resonant decomposition' to show global well-posedness results for small-in-$L^2$ initial data belonging to some spaces weaker than the energy class. We also consider an application of our ideas to the initial value problem on $\mathbb{R}^2$ and give an improvement of the best known result by Pecher (2012).

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Nobu Kishimoto. 2012-03-28. Resonant decomposition and the $I$-method for the two-dimensional Zakharov system. https://arxiv.org/abs/1203.6376

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