Well-posedness for the KdV hierarchy
Klaus, Friedrich
1; Koch, Herbert; Liu, Baoping
1 Institut für Analysis (IANA), Karlsruher Institut für Technologie (KIT)
1; Koch, Herbert; Liu, Baoping1 Institut für Analysis (IANA), Karlsruher Institut für Technologie (KIT)
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.
(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.
| Zugehörige Institution(en) am KIT | Institut für Analysis (IANA) Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsmonat/-jahr | 11.2023 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X KITopen-ID: 1000165073 |
| Verlag | Karlsruher Institut für Technologie (KIT) |
| Umfang | 139 S. |
| Serie | CRC 1173 Preprint ; 2023/23 |
| Projektinformation | SFB 1173/3 (DFG, DFG KOORD, SFB 1173/3) |
| Externe Relationen | Siehe auch |