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arXiv · 1805.07604

A note on global existence for the Zakharov system on $\mathbb{T}$

E. Compaan
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Abstract

We show that the one-dimensional periodic Zakharov system is globally well-posed in a class of low-regularity Fourier-Lebesgue spaces. The result is obtained by combining the I-method with Bourgain's high-low decomposition method. As a corollary, we obtain probabilistic global existence results in $L^2$-based Sobolev spaces. We also obtain global well-posedness in $H^{\frac12+} \times L^2$, which is sharp (up to endpoints) in the class of $L^2$-based Sobolev spaces.

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E. Compaan. 2018-05-19. A note on global existence for the Zakharov system on $\mathbb{T}$. https://arxiv.org/abs/1805.07604

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