The conservative Camassa-Holm flow with step-like irregular initial data

Eckhardt, Jonathan (avtor), Kostenko, Aleksej Sergejevič (avtor)

We extend the inverse spectral transform for the conservative Camassa-Holm flow on the line to a class of initial data that requires strong decay at one endpoint but only mild boundedness-type conditions at the other endpoint. The latter condition appears to be close to optimal in a certain sense for the well-posedness of the conservative Camassa-Holm flow. As a byproduct of our approach, we also find a family of new (almost) conservation laws for the Camassa-Holm equation, which could not be deduced from its bi-Hamiltonian structure before and which are connected to certain Besov-type norms (however, in a rather involved way). These results appear to be new even under positivity assumptions on the corresponding momentum, in which case the conservative Camassa-Holm flow coincides with the classical Camassa-Holm flow and no blow-ups occur.

• Jezik: Angleški jezik
• Ključne besede: conservative Camassa-Holm flow, inverse spectral transform
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.05.2025
• Leto izida: 2025
• Št. strani: 42 str.
• Številčenje: Vol. 130, iss. 5, article no. e70050
• PID: 20.500.12556/RUL-175177
• UDK: 517.9
• ISSN pri članku: 0024-6115
• DOI: 10.1112/plms.70050
• COBISS.SI-ID: 236509955
• Datum objave v RUL: 20.10.2025

Gradivo je del revije

• Naslov: Proceedings of the London Mathematical Society
• Skrajšan naslov: Proc. Lond. Math. Soc.
• Založnik: Wiley, London Mathematical Society
• ISSN: 0024-6115
• COBISS.SI-ID: 26179584

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Projekti

• Financer: FWF - Austrian Science Fund
• Številka projekta: I4600

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: N1-0137
• Naslov: Nelinearni Valovi in Spektralna Teorija