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arXiv · 2309.12773

Wellposedness for the KdV hierarchy

Friedrich Klaus·Herbert Koch·Baoping Liu
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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. Section 2 has been rewritten. Typos corrected-

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Friedrich Klaus, Herbert Koch, Baoping Liu. 2023-09-22. Wellposedness for the KdV hierarchy. https://arxiv.org/abs/2309.12773

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