The conservative Camassa-Holm flow with step-like irregular initial dataEckhardt, Jonathan (Avtor) Kostenko, Aleksej Sergejevič (Avtor) conservative Camassa-Holm flowinverse spectral transformWe 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.20252025-10-20 13:36:28Članek v reviji175177UDK: 517.9ISSN pri članku: 0024-6115DOI: 10.1112/plms.70050COBISS_ID: 236509955sl