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Volume 2, Number 1, 2012, Pages 11-28                                                                DOI:10.11948/2012002
Cauchy problem for the Zakharov System Arising from Ion-Acoustic Modes with low regularity data
Boling Guo,Lijia Han,Zaihui Gan
Keywords:Zaklarov system
Abstract:
      We prove local well-posedness results for the Zakharov System Arising from Ion-Acoustic Modes in two spacial dimension with large initial data in low regularity Sobolev space \(   (\dot{H}^1 \bigcup H^{\frac{1}{2}})\times L^2 \times H^{-1}  \).  Using ”derivative sharing”, the local well-posedness results in \( (\dot{H}^1 \bigcup H^{\frac{1}{2}-\delta})\times H^{\delta} \times H^{-1+\delta}\)  are also obtained, for any  0 \(\leq \delta \leq 1/2 \).
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