Long-time asymptotics for polymerization models Calvo Yagüe, Juan Doumic, Marie Perthame, Benoît Lifshitz-Slyozov Long-time behavior Ostwald ripening Nucleation Polymerization Nonlinear transport equation The final publication is available at link.springer.com/article/10.1007/s00220-018-3218-5 This study is devoted to the long-term behavior of nucleation, growth and fragmentation equations, modeling the spontaneous formation and kinetics of large polymers in a spatially homogeneous and closed environment. Such models are, for instance, commonly used in the biophysical community in order to model in vitro experiments of fibrillation. We investigate the interplay between four processes: nucleation, polymerization, depolymerization and fragmentation. We first revisit the well-known Lifshitz– Slyozov model, which takes into account only polymerization and depolymerization, and we show that, when nucleation is included, the system goes to a trivial equilibrium: all polymers fragmentize, going back to very small polymers. Taking into account only polymerization and fragmentation, modeled by the classical growth-fragmentation equation, also leads the system to the same trivial equilibrium, whether or not nucleation is considered. Finally, when taking into account a depolymerization reaction term, we prove the existence of a steady size-distribution of polymers, as soon as polymerization dominates depolymerization for large sizes whereas depolymerization dominates polymerization for smaller ones—a case which fits the classical assumptions for the Lifshitz–Slyozov equations, but complemented with fragmentation so that “Ostwald ripening” does not happen. 2024-02-03T18:54:29Z 2024-02-03T18:54:29Z 2018 journal article Communications in Mathematical physics 363, 111-137 https://hdl.handle.net/10481/88045 10.1007/s00220-018-3218-5 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Springer