Asymptotic Completeness for Relativistic Kinetic Equations with Short-range Interaction Forces

Ha, Seung‐Yeal; Kim, Yong Duck; Lee, Ho; Noh, Se Eun

doi:10.4310/maa.2007.v14.n3.a3

Cited by 15 publications

(11 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Conditional asymptotic completeness for the relativistic Boltzmann equation was shown in 2007 [36]; the existence theorem from [27] does not allow the kind of decay which would be needed for the result of [36]. It is these three results [11,27,36] on the relativistic Boltzmann equation that our theorems below can extend.…”

Section: The Relativistic Boltzmann Equation Is the Central Equation mentioning

confidence: 91%

Global Newtonian Limit for the Relativistic Boltzmann Equation near Vacuum

Strain¹

2010

SIAM J. Math. Anal.

View full text Add to dashboard Cite

We study the Cauchy Problem for the relativistic Boltzmann equation with near Vacuum initial data. Unique global in time mild solutions are obtained uniformly in the speed of light parameter c ≥ 1. We furthermore prove that solutions to the relativistic Boltzmann equation converge to solutions of the Newtonian Boltzmann equation in the limit as c → ∞ on arbitrary time intervals [0, T ], with convergence rate 1/c 2−ǫ for any ǫ ∈ (0, 2). This may be the first proof of unique global in time validity of the Newtonian limit for a Kinetic equation.

show abstract

Section: The Relativistic Boltzmann Equation Is the Central Equation mentioning

confidence: 91%

Global Newtonian Limit for the Relativistic Boltzmann Equation near Vacuum

Strain¹

2010

SIAM J. Math. Anal.

View full text Add to dashboard Cite

show abstract

“…Let us point out studies of the Newtonian limit [5,44] for the Boltzmann equation. We mention theories of unique global in time solutions with initial data that is "near Vacuum" as in [24,29,44]. Andréasson, Calogero and Illner [2] prove that there can be blow-up in the presence of only the gain term.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Coordinates in the relativistic Boltzmann theory

Strain¹

2011

Kinetic &Amp; Related Models

View full text Add to dashboard Cite

It is often the case in mathematical analysis that solving an open problem can be facilitated by finding a new set of coordinates which may illumniate the known difficulties. In this article, we illustrate how to derive an assortment coordinates in which to represent the relativistic Boltzmann collision operator. We show the equivalence between some known representations, and others which seem to be new. One of these representations has been used recently to solve several open problems.Comment: 16 pages, to appear in the issue of K.R.M. dedicated to the memory of Carlo Cercignan

show abstract

“…In particular [1] proves the strong L 1 convergence to a relativistic Maxwellian, after taking a subsequence, for weak solutions with large initial data that is not necessarily close to an equilibrium solution. There are also results in the context of local [7] and global [49] Newtonian limits, and near Vacuum results [22,35,49] and blow-up [2] for the gain term only. We also mention a study of the collision map and the pre-post collisional change of variables in [23].…”

Section: Introductionmentioning

confidence: 90%

Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials

Strain

2010

Commun. Math. Phys.

114

View full text Add to dashboard Cite

In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out sufficiently close in L ∞ ℓ . If the initial data are continuous then so is the corresponding solution. We work in the case of a spatially periodic box. Conditions on the collision kernel are generic in the sense of [18]; this resolves the open question of global existence for the soft potentials.

show abstract

Asymptotic Completeness for Relativistic Kinetic Equations with Short-range Interaction Forces

Cited by 15 publications

References 20 publications

Global Newtonian Limit for the Relativistic Boltzmann Equation near Vacuum

Global Newtonian Limit for the Relativistic Boltzmann Equation near Vacuum

Coordinates in the relativistic Boltzmann theory

Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials

Contact Info

Product

Resources

About