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On the dynamics of correlations in Scaling limits of interacting particle systems

dc.contributor.advisorVelázquez, Juan J. L.
dc.contributor.authorWinter, Raphael Elias
dc.date.accessioned2020-04-25T02:52:27Z
dc.date.available2020-04-25T02:52:27Z
dc.date.issued09.07.2018
dc.identifier.urihttp://hdl.handle.net/20.500.11811/7567
dc.description.abstractIn this work, we analyze the properties of two-particle correlations in the weak-coupling and plasma limit of interacting particle systems motivated by Bogolyubov's formal derivation of kinetic equations.
We prove that the leading order evolution in the weak-coupling scaling limit is stable on the macroscopic timescale, and yields the nonlinear Landau equation as kinetic equation. This result shows the transition from the non-Markovian dynamics of the interacting particle system to the Markovian, parabolic evolution in the kinetic limit. Since the system is non-dissipative before taking the limit, we introduce a time-averaged notion of stability to derive an a priori estimate on the solution.
Moreover, we prove the global stability of the truncated correlation function in the plasma limit, for a time independent background distribution and soft potentials. In the case of systems with Coulombian interaction, we prove the onset of the Debye screening length and show that the limit evolution is driven by the interaction of particles with impact parameter much smaller than the Debye length.
dc.language.isoeng
dc.rightsIn Copyright
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectKinetische Gleichungen
dc.subjectLandau-Gleichung
dc.subjectVlasov-Gleichung
dc.subjectBBGKY-Hierarchie
dc.subjectPartielle Differentialgleichungen
dc.subject.ddc510 Mathematik
dc.titleOn the dynamics of correlations in Scaling limits of interacting particle systems
dc.typeDissertation oder Habilitation
dc.publisher.nameUniversitäts- und Landesbibliothek Bonn
dc.publisher.locationBonn
dc.rights.accessRightsopenAccess
dc.identifier.urnhttps://nbn-resolving.org/urn:nbn:de:hbz:5n-50822
ulbbn.pubtypeErstveröffentlichung
ulbbnediss.affiliation.nameRheinische Friedrich-Wilhelms-Universität Bonn
ulbbnediss.affiliation.locationBonn
ulbbnediss.thesis.levelDissertation
ulbbnediss.dissID5082
ulbbnediss.date.accepted2018-05-14
ulbbnediss.instituteMathematisch-Naturwissenschaftliche Fakultät : Fachgruppe Mathematik / Institut für angewandte Mathematik
ulbbnediss.fakultaetMathematisch-Naturwissenschaftliche Fakultät
dc.contributor.coRefereeNiethammer, Barbara


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