Time evolution of infinitely many particles: An existence theorem

Calderoni, P.; Caprino, S.

doi:10.1007/bf01011882

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Introduction Statement Of the Problem And Main Results1

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Cited by 11 publications

(3 citation statements)

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“…In particular, we are interested in the time evolution of nonequilibrium statistical states [1][2][3][4][5][6][7][8][9][10][11][12][13]. The difficulty of the problem is related to the dimension of the space and the kind of mutual interaction among the particles.…”

Section: Introduction and Resultsmentioning

confidence: 99%

Time Evolution of Two Dimensional Systems with Infinitely Many Particles Mutually Interacting via Very Singular Forces

2012

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Section: Introduction and Resultsmentioning

confidence: 99%

Time Evolution of Two Dimensional Systems with Infinitely Many Particles Mutually Interacting via Very Singular Forces

2012

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“…It is not obvious that this system cannot have a blow-up, that is a collapse of infinite mass in a finite region and/or an unbounded growth of the velocity. Actually for point particles the problem has been solved many years ago, when the problem of the dynamics of infinitely many particles has been faced (see [1,2,5,6,7,11,12,18,20,21,22,27,28,29,32,33,39,45,46,47] and for a short review [9]). The solution depends on the dimensions and the shape of the region in which the motion happens (the unbounded cylinder case is treated in [6]).…”

Section: Introduction Statement Of the Problem And Main Resultsmentioning

confidence: 99%

Time Evolution of an Infinitely Extended Vlasov System with Singular Mutual Interaction

2015

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We study the time evolution of an infinitely extended system in the mean field approximation, governed by the Vlasov equation. This system is confined in an unbounded cylinder by an external force singular on the border. The mutual interaction is assumed singular at short distance as 1/r α with α < 2/3 (or α < 1 in case of an external Lorentz force) and with a short range. The initial density is assumed bounded. Differently from studies which assume initial data compact in space and/or in velocities, here we consider a system having infinite mass and an exponential bound on the velocities, according to the Maxwell-Boltzmann law.

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“…The existence of the time evolution for systems composed by infinitely many particles moving according to Newton's laws of motion is a classical issue in non-equilibrium statistical mechanics, and several studies have been devoted to this subject, see, e.g., [3,7,8,11,12,14,20,21,24,25,27]. For a summary, see for instance Appendix 1 of [9].…”

Section: Introductionmentioning

confidence: 99%