Herbert Koch, University of Bonn
In this talk I report on joint work with Baoping Liu and Friedrich Klaus. We prove existence and uniqueness of weak solutions to all equations in the Gardner hierarchy for initial data in L^2(R). As a consequence we obtain uniqueness of weak solutions to all equations of the Korteweg-de Vries hierarchy for L^2(R) initial data and a continuous extension of the flows to H^1.
The proof makes heavy use of the Miura map and of the commuting vector field method of Killip and Visan.