| 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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