The KdV hierarchy at H^{-1} regularity

This is a report on joint work with Friedrich Klaus and Baoping Liu. We prove wellposedness for all equations of the KdV hierarchy in H^{-1}. The proof follows the outline of Killip and Visan for KdV: We prove tightness, and convergence of the difference flow simultaneously for all equations of the hierarchy.

In contrast to Killip and Visan we reduce the problem via a modified Miura map to the Gardner hierarchy.

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