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KRM publishes high quality papers of original research in the areas of kinetic equations spanning from mathematical theory to numerical analysis, simulations and modelling. It includes studies on models arising from physics, engineering, finance, biology, human and social sciences, together with their related fields such as fluid models, interacting particle systems and quantum systems. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time.
KRM was launched in 2008 and is edited by a group of energetic leaders to guarantee the journal's highest standard and closest link to the scientific communities. A unique feature of this journal is its streamlined review process and rapid publication. Authors are kept informed throughout the process through direct and personal communication between the authors and editors.
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 Publishes 4 issues a year in March, June, September and December.
 Publishes online only.
 Indexed in Science Citation Index, ISI Alerting Services, CompuMath Citation Index, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), INSPEC, Mathematical Reviews, MathSciNet, PASCAL/CNRS, Scopus, Web of Science and Zentralblatt MATH.
 Archived in Portico and CLOCKSS.
 KRM is a publication of the American Institute of Mathematical Sciences. All rights reserved.

TOP 10 Most Read Articles in KRM, October 2017
1 
On the dynamics of social conflicts: Looking for the black swan
Volume 6, Number 3, Pages: 459  479, 2013
Nicola Bellomo,
Miguel A. Herrero
and Andrea Tosin
Abstract
References
Full Text
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This paper deals with the modeling of social competition, possibly resulting in the onset of extreme conflicts. More precisely, we discuss models describing the interplay between individual competition for wealth distribution that, when coupled with political stances coming from support or opposition to a Government, may give rise to strongly selfenhanced effects. The latter may be thought of as the early stages of massive unpredictable events known as Black Swans, although no analysis of any fullydeveloped Black Swan is provided here. Our approach makes use of the framework of the kinetic theory for active particles, where nonlinear interactions among subjects are modeled according to gametheoretical principles.

2 
Existence and sharp localization in velocity
of smallamplitude Boltzmann shocks
Volume 2, Number 4, Pages: 667  705, 2009
Guy Métivier
and K. Zumbrun
Abstract
Full Text
Related Articles
Using a weighted $H^s$contraction mapping argument based on the
macromicro decomposition of Liu and Yu, we give an elementary proof
of existence, with sharp rates of decay and distance from the
ChapmanEnskog approximation, of smallamplitude shock profiles of
the Boltzmann equation with hardsphere potential, recovering and
slightly sharpening results obtained by Caflisch and Nicolaenko
using different techniques. A key technical point in both analyses
is that the linearized collision operator $L$ is negative definite
on its range, not only in the standard squareroot Maxwellian
weighted norm for which it is selfadjoint, but also in norms with
nearby weights. Exploring this issue further, we show that $L$ is
negative definite on its range in a much wider class of norms
including norms with weights asymptotic nearly to a full Maxwellian
rather than its square root. This yields sharp localization in
velocity at nearMaxwellian rate, rather than the squareroot rate
obtained in previous analyses.

3 
Unstable galaxy models
Volume 6, Number 4, Pages: 701  714, 2013
Zhiyu Wang,
Yan Guo,
Zhiwu Lin
and Pingwen Zhang
Abstract
References
Full Text
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The dynamics of collisionless galaxy can be described by the VlasovPoisson
system. By the Jean's theorem, all the spherically symmetric steady galaxy
models are given by a distribution of $\Phi(E,L)$, where $E$ is the particle
energy and $L$ the angular momentum. In a celebrated DoremusFeixBaumann
Theorem [7], the galaxy model $\Phi(E,L)$ is stable if the
distribution $\Phi$ is monotonically decreasing with respect to the particle
energy $E.$ On the other hand, the stability of $\Phi(E,L)$ remains largely
open otherwise. Based on a recent abstract instability criterion of GuoLin
[11], we constuct examples of unstable galaxy models of $f(E,L)$ and
$f\left( E\right) \ $in which $f$ fails to be monotone in $E.$

4 
Kinetic theory and numerical simulations of twospecies coagulation
Volume 7, Number 2, Pages: 253  290, 2014
Carlos Escudero,
Fabricio Macià,
Raúl Toral
and Juan J. L. Velázquez
Abstract
References
Full Text
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In this work we study the stochastic process of twospecies
coagulation. This process consists in the aggregation dynamics
taking place in a ring. Particles and clusters of particles are set
in this ring and they can move either clockwise or counterclockwise.
They have a probability to aggregate forming larger clusters when
they collide with another particle or cluster. We study the
stochastic process both analytically and numerically. Analytically,
we derive a kinetic theory which approximately describes the process
dynamics. One of our strongest assumptions in this respect
is the so called wellstirred limit, that allows neglecting the
appearance of spatial coordinates in the theory, so this becomes
effectively reduced to a zeroth dimensional model.
We determine the long time behavior of such a model, making emphasis
in one special case in which it displays selfsimilar solutions.
In particular these calculations
answer the question of how the system gets ordered, with all
particles and clusters moving in the same direction, in the long
time. We compare our analytical results with direct numerical
simulations of the stochastic process and both corroborate its
predictions and check its limitations. In particular, we numerically
confirm the ordering dynamics predicted by the kinetic theory and
explore properties of the realizations of the stochastic process
which are not accessible to our theoretical approach.

5 
Asymptotic preserving scheme for a kinetic model describing incompressible fluids
Volume 9, Number 1, Pages: 51  74, 2015
Nicolas Crouseilles,
Mohammed Lemou,
SV Raghurama Rao,
Ankit Ruhi
and Muddu Sekhar
Abstract
References
Full Text
Related Articles
The kinetic theory of fluid turbulence modeling developed by Degond and Lemou in [7]
is considered for further study, analysis and simulation. Starting with the Boltzmann like equation representation for
turbulence modeling, a relaxation type collision term is introduced for isotropic turbulence. In order to describe some important turbulence phenomenology, the relaxation time incorporates a dependency on the turbulent microscopic energy and this makes difficult the construction of efficient numerical methods. To investigate this problem, we focus here on a multidimensional prototype model and first propose an appropriate change of frame that
makes the numerical study simpler. Then, a numerical strategy to tackle the stiff relaxation source term
is introduced in the spirit of Asymptotic Preserving Schemes. Numerical tests are performed in a onedimensional
framework on the basis of the developed strategy to confirm its efficiency.

6 
Global existence and semiclassical limit for quantum hydrodynamic equations with viscosity and heat conduction
Volume 9, Number 1, Pages: 165  191, 2015
Xueke Pu
and Boling Guo
Abstract
References
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The hydrodynamic equations with quantum effects are studied in this paper. First we establish the global existence of smooth solutions with small initial data and then in the second part, we establish the convergence of the solutions of the quantum hydrodynamic equations to those of the classical hydrodynamic equations. The energy equation is considered in this paper, which added new difficulties to the energy estimates, especially to the selection of the appropriate Sobolev spaces.

7 
The Cauchy problem for 1D compressible flows with densitydependent viscosity coefficients
Volume 1, Number 2, Pages: 313  330, 2008
Quansen Jiu
and Zhouping Xin
Abstract
Full Text
Related Articles
This paper concerns with Cauchy problems for the onedimensional
compressible NavierStokes equations with densitydependent
viscosity coefficients. Two cases are considered here, first, the
initial density is assumed to be integrable on the whole real
line. Second, the deviation of the initial density from a positive
constant density is integrable on the whole real line. It is
proved that for both cases, weak solutions for the Cauchy problem
exist globally in time and the large time asymptotic behavior of
such weak solutions are studied. In particular, for the second
case, the phenomena of vanishing of vacuum and blowup of the
solutions are presented, and it is also shown that after the
vanishing of vacuum states, the globally weak solution becomes a
unique strong one. The initial vacuum is permitted and the results
apply to the onedimensional SaintVenant model for shallow water.

8 
Propagation of chaos for the spatially homogeneous Landau equation for Maxwellian molecules
Volume 9, Number 1, Pages: 1  49, 2015
Kleber Carrapatoso
Abstract
References
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We prove a quantitative propagation of chaos and entropic chaos, uniformly in time, for the spatially homogeneous Landau equation in the case of Maxwellian molecules. We improve the results of Fontbona, Guérin and Méléard [9] and Fournier [10] where the propagation of chaos is proved for finite time. Moreover, we prove a quantitative estimate on the rate of convergence to equilibrium uniformly in the number of particles.

9 
Stability of a VlasovBoltzmann binary mixture at the phase transition on an interval
Volume 6, Number 4, Pages: 761  787, 2013
Raffaele Esposito,
Yan Guo
and Rossana Marra
Abstract
References
Full Text
Related Articles
We consider a kinetic model for a system of two species of particles on a sufficiently large periodic interval, interacting through a long range repulsive potential and by collisions. The model is described by a set of two coupled VlasovBoltzmann equations. For temperatures below the critical value and suitably prescribed masses, there is a non homogeneous solution, the double soliton, which is a minimizer of the entropy functional. We prove the stability, up to translations, of the double soliton under small perturbations. The same arguments imply the stability of the pure phases, as well as the stability of the mixed phase above the critical temperature. The mixed phase is proved to be unstable below the critical temperature.

10 
Stability of viscous shock wave for compressible
NavierStokes equations with free boundary
Volume 3, Number 3, Pages: 409  425, 2010
Feimin Huang,
Xiaoding Shi
and Yi Wang
Abstract
Full Text
Related Articles
A free boundary problem for the onedimensional compressible NavierStokes equations in Eulerian coordinate is investigated.
The stability of the viscous
shock wave to the free boundary problem is established under some smallness conditions. The proof is given
by an elementary energy method.

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