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For $k\\geq8$, local well-posedness is shown to hold for data in $H^s(\\mathbb{R}^2)$, $s>s_k$, where $s_k=1-3/(2k-4)$. 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For $k\\geq8$, local well-posedness is shown to hold for data in $H^s(\\mathbb{R}^2)$, $s>s_k$, where $s_k=1-3/(2k-4)$. 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