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L^2-concentration phenomenon for Zakharov system below energy norm

Daoyuan Fang·Sijia Zhong
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Abstract

In this paper, we'll prove a L^2-concentration result of Zakharov system in space dimension two, with radial initial data (u_0,n_0,n_1)\in H^s\times L^2\times H^{-1} ({16/17}<s<1), when blow up of the solution happens by I-method. In additional to that we find a blow up character of this system. Furthermore, we improve the global existence result of Bourgain's to above spaces.

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Daoyuan Fang, Sijia Zhong. 2007-02-07. L^2-concentration phenomenon for Zakharov system below energy norm. https://arxiv.org/abs/math/0702181

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