A-priori bounds for KdV equation below $H^{-3/4}$

preprint2011arXivOpen access

We consider the Korteweg-de Vries Equation (KdV) on the real line, and prove that the smooth solutions satisfy a-priori local in time $H^s$ bound in terms of the $H^s$ size of the initial data for $s\geq -4/5$ .

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A-priori bounds for KdV equation below $H^{-3/4}$

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A-priori bounds for KdV equation below H−3/4H^{-3/4}H−3/4

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A-priori bounds for KdV equation below $H^{-3/4}$