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.
Sharp ill-posedness results for the KdV and mKdV e quations on the torus
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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.