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Studies of the relativistic Vlasov-Poisson system
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Young, Brent Oneil Joseph. Studies of the relativistic Vlasov-Poisson system. Retrieved from https://doi.org/doi:10.7282/T39G5M3D

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TitleStudies of the relativistic Vlasov-Poisson system
NameYoung, Brent Oneil Joseph (author); Kiessling, Michael K (chair); Tahvildar-Zadeh, Abdolre S (internal member); Carlen, Eric A (internal member); Spohn, Herbert (outside member); Rutgers University; Graduate School - New Brunswick
Date Created2011
Other Date2011-05 (degree)
SubjectMathematics, Quantum field theory, Relativistic quantum theory
Extentix, 100 p. : ill.
DescriptionWe examine several questions pertaining to the relativistic Vlasov-Poisson system withattractive coupling (rVP−) raised in a recent paper [KTZ08] by Kiessling and Tahvildar-Zadeh (KTZ). First, KTZ proved that for everyβ≥3/2 there is a critical, non-zerovalueC−βsuch that certain initial data withLβnorm less thanC−βlaunch solutionsto rVP−which exist globally in time. The authors obtained the sharp value forC−3/2and characterized the remaining constants via a minimization problem. We show theexistence of minimizers and calculateC−βforβ >3/2.

Second, KTZ proved that any spherically symmetric classical solution of rVP−launched by zero energy initial data with virial≤ −1/2 will blow up in finite time.However, Simone Calogero has raised the question whether any such data exist at all.We settle this question by constructing two different classes of such initial data.

Third, we examine the recent proposal in [KTZ08] whereby rVP−might be derivedfrom an overall neutral two-specie, spherically symmetric plasma with initial conditionchoseniidin both species, interacting through regularized electromagnetic fieldsonspace-time scales not typically considered in Vlasov-type limits.We show first that onthe usual scales the familiar relativistic Vlasov-Poisson system for an overall neutraltwo-specie plasma is obtained if the particles of each specie are separately choseniidbyf+0andf−0respectively. Iff+0=f−0this dynamics reduces to trivial free-streaming of all particles, withf+t=f−tfor all later times (on this Vlasov scale). To see non-trivialplasma dynamics, the usual procedure would be to look at longer time scales and tocorrect the dynamics by adding a “relativistic” generalization of the Lenard-Balescu“collision” operator to the free-streaming Vlasov operator. The proposal in [KTZ08] isthat instead of the collision operator, the rVP−force term of a single specie Newtonsystem could emerge on thea prioriscales. We examine this proposal for the simplercase of purely Coulombic interactions. We will extract from this reduced model evidenceforbothan rVP−force term and a dissipative operator that govern the dynamics.
NotePh.D.
NoteIncludes bibliographical references
NoteIncludes vita
Noteby Brent Oneil Joseph Young
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T39G5M3D
Languageeng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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