A priori bounds for KdV equation below \(H^{- \frac{3}{4}}\). (English) Zbl 1308.35251
Summary: 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 \(s \geq - \frac{4}{5}\).
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35B45 | A priori estimates in context of PDEs |
| 35D30 | Weak solutions to PDEs |
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