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

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

2012-03-28

arxiv.org/abs/1203.6376v1

Mathematics

Analysis of PDEs

29 pages

Scientific paper

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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