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arxiv: 2309.12773 · v2 · submitted 2023-09-22 · 🧮 math.AP

Wellposedness for the KdV hierarchy

Friedrich Klaus , Herbert Koch , Baoping Liu This is my paper
classification 🧮 math.AP
keywords gardnerhierarchyenergiesequationgeneratingwellposednessallowsapproximate
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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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  1. A priori bounds and equicontinuity of orbits for the intermediate long wave equation

    math.AP 2025-06 unverdicted novelty 6.0

    Uniform a priori H^s bounds and equicontinuity of orbits are proved for the intermediate long wave equation in -1/2 < s ≤ 0 on the line and circle via a Lax pair formulation.