Proves wellposedness in H^{-1} for the full KdV hierarchy by relating it to the Gardner hierarchy via the Miura map and applying Kato smoothing estimates.
On the hierarchies of higher order mKdV and KdV equa- tions
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Wellposedness for the KdV hierarchy
Proves wellposedness in H^{-1} for the full KdV hierarchy by relating it to the Gardner hierarchy via the Miura map and applying Kato smoothing estimates.