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Wellposedness for the KdV hierarchy (2309.12773v1)
Published 22 Sep 2023 in math.AP
Abstract: We prove a version of wellposedness for all equations of the KdV hierarchy in $H{-1}$. Ingredients are 1) The Miura map which allows to define the Gardner hierarchy through the generating function of the energies so that the $N$th Gardner equation is equivalent to the $N$th KdV equation. 2) A rigorous relation between the generating functions of the energies and the KdV resp. Gardner Hamiltonians. 3) Kato smoothing estimates for weak solutions and approximate flows.
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