SMF RC. Kinetic theory and fluid mechanics: couplings, scalings and asymptotics. / ER SMF. Théorie cinétique et mécanique des fluides : couplages, échelles et asymptotiques.

Collection SMF RC. Kinetic theory and fluid mechanics: couplings, scalings and asymptotics. / ER SMF. Théorie cinétique et mécanique des fluides : couplages, échelles et asymptotiques.

Organizer(s) Han-Kwan, Daniel ; Lods, Bertrand ; Moussa, Ayman ; Tristani, Isabelle

Date(s) 24/03/2025 - 28/03/2025

linked URL https://conferences.cirm-math.fr/3205.html

00:00:00 / 00:00:00

3 5

Recent advances on the Smoluchowski coagulation equation under non-equilibrium conditions

By Alessia Nota

The Smoluchowski's coagulation equation is an integro-differential equation of kinetic type which provides a mean-field description for mass aggregation phenomena. In this talk I will present some recent results on the problem of existence or non-existence of stationary solutions, both for single and multi-component systems, under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. The most striking feature of these stationary solutions is that, whenever they exist, the solutions to multi-component systems exhibit an unusual “spontaneous localization” phenomenon: they localize along a line in the composition space as the total size of the particles increase. This localization is a universal property of multicomponent systems and it has also been recently proved to occur in time dependent solutions to mass conserving coagulation equations.

Information about the video

Date of recording 25/03/2025
Date of publication 04/04/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20331903
Cite this video Nota, Alessia (25/03/2025). Recent advances on the Smoluchowski coagulation equation under non-equilibrium conditions. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20331903
URL https://dx.doi.org/10.24350/CIRM.V.20331903

Domain(s)

Bibliography

FERREIRA, Marina A., LUKKARINEN, Jani, NOTA, Alessia, et al. Stationary non-equilibrium solutions for coagulation systems. Archive for Rational Mechanics and Analysis, 2021, vol. 240, p. 809-875. - https://doi.org/10.1007/s00205-021-01623-w
FERREIRA, Marina A., LUKKARINEN, Jani, NOTA, Alessia, et al. Localization in stationary non-equilibrium solutions for multicomponent coagulation systems. Communications in Mathematical Physics, 2021, vol. 388, p. 479-506. - https://doi.org/10.1007/s00220-021-04201-z
FERREIRA, Marina A., LUKKARINEN, Jani, NOTA, Alessia, et al. Non-equilibrium stationary solutions for multicomponent coagulation systems with injection. Journal of Statistical Physics, 2023, vol. 190, no 5, p. 98. - https://doi.org/10.1007/s10955-023-03107-5
FERREIRA, Marina A., LUKKARINEN, Jani, NOTA, Alessia, et al. Asymptotic localization in multicomponent mass conserving coagulation equations. Pure and Applied Analysis, 2024, vol. 6, no 3, p. 731-764. - https://doi.org/10.2140/paa.2024.6.731

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