20.500.12556/RUL-175177 The conservative Camassa-Holm flow with step-like irregular initial data 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. conservative Camassa-Holm flow inverse spectral transform true false true Angleški jezik Angleški jezik Članek v reviji 2025-10-20 13:36:28 2025-10-20 13:36:33 2025-12-07 03:47:44 0000-00-00 00:00:00 2025 0 0 42 str. iss. 5, article no. e70050 Vol. 130 May 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-05-01 517.9 0024-6115 10.1112/plms.70050 236509955 Proceedings_of_London_Math_Soc_-_2025_-_Eckhardt_-_The_conservative_Camassa_Holm_flow_with_step‐like_irregular_initial_data.pdf Proceedings_of_London_Math_Soc_-_2025_-_Eckhardt_-_The_conservative_Camassa_Holm_flow_with_step‐like_irregular_initial_data.pdf 1 141A7E78684A805536E4853889CD7E5F 5226cf5854843eadb48a4af9442881506152fbaf2c76a1d826dd0620651efdee 12dd784b-ada9-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=220488 https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.70050 1 c58a063f-ada8-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=220487 Fakulteta za matematiko in fiziko 0 0 0