The talk reports on joint work with B. Liu und F. Klaus. In a seminal paper Killip and Visan have proven wellposedness for the KdV equation in H^{-1}. We extent the result to the full hierarchy.
Crucial ingredients are the Miura map, which translates the problem to the Gardner hierarchy in L2 and introduces a natural spectral parameter. We prove existence and uniqueness of weak solutions to all equations of the Gardner hierarchy for initial data in L^2.