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Kinetic and Related Models最新文献

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Propagation of chaos: A review of models, methods and applications. I. Models and methods 混沌的传播:模型、方法和应用综述。1、模型与方法
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2022-02-23 DOI: 10.3934/krm.2022017
L. Chaintron, A. Diez
{"title":"Propagation of chaos: A review of models, methods and applications. I. Models and methods","authors":"L. Chaintron, A. Diez","doi":"10.3934/krm.2022017","DOIUrl":"https://doi.org/10.3934/krm.2022017","url":null,"abstract":"The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods as well as several important results in the field. The models considered include the McKean-Vlasov diffusion, the mean-field jump models and the Boltzmann models. The first part of this review is an introduction to modelling aspects of stochastic particle systems and to the notion of propagation of chaos. The second part presents concrete applications and a more detailed study of some of the important models in the field.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91247514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 36
Global-in-time existence of weak solutions for Vlasov-Manev-Fokker-Planck system Vlasov-Manev-Fokker-Planck系统弱解的全局实时存在性
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2022-02-17 DOI: 10.3934/krm.2022021
Young-Pil Choi, In-Jee Jeong
{"title":"Global-in-time existence of weak solutions for Vlasov-Manev-Fokker-Planck system","authors":"Young-Pil Choi, In-Jee Jeong","doi":"10.3934/krm.2022021","DOIUrl":"https://doi.org/10.3934/krm.2022021","url":null,"abstract":"<p style='text-indent:20px;'>We consider the Vlasov–Manev–Fokker–Planck (VMFP) system in three dimensions, which differs from the Vlasov–Poisson–Fokker–Planck in that it has the gravitational potential of the form <inline-formula><tex-math id=\"M1\">begin{document}$ -1/r - 1/r^2 $end{document}</tex-math></inline-formula> instead of the Newtonian one. For the VMFP system, we establish the global-in-time existence of weak solutions under smallness assumption on either the initial mass or the coefficient of the pure Manev potential. The proof extends to several related kinetic systems.</p>","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77550478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Local well-posedness for a class of singular Vlasov equations 一类奇异Vlasov方程的局部适定性
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2022-02-15 DOI: 10.3934/krm.2022027
Thomas Chaub
{"title":"Local well-posedness for a class of singular Vlasov equations","authors":"Thomas Chaub","doi":"10.3934/krm.2022027","DOIUrl":"https://doi.org/10.3934/krm.2022027","url":null,"abstract":"<p style='text-indent:20px;'>In this article we study a singular Vlasov system on the torus where the force field has the smoothness of a (fractional) derivative <inline-formula><tex-math id=\"M1\">begin{document}$ D^{alpha} $end{document}</tex-math></inline-formula> of the density, where <inline-formula><tex-math id=\"M2\">begin{document}$ alpha>0 $end{document}</tex-math></inline-formula>. We prove local well-posedness in Sobolev spaces without restriction on the data. This is in sharp contrast with the case <inline-formula><tex-math id=\"M3\">begin{document}$ alpha = 0 $end{document}</tex-math></inline-formula> which is ill-posed in Sobolev spaces for general data.</p>","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82804703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence of large-data global weak solutions to kinetic models of nonhomogeneous dilute polymeric fluids 非均相稀聚流体动力学模型大数据全局弱解的存在性
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2022-02-14 DOI: 10.3934/krm.2023018
Chuhui He, E. Suli
{"title":"Existence of large-data global weak solutions to kinetic models of nonhomogeneous dilute polymeric fluids","authors":"Chuhui He, E. Suli","doi":"10.3934/krm.2023018","DOIUrl":"https://doi.org/10.3934/krm.2023018","url":null,"abstract":"We prove the existence of large-data global-in-time weak solutions to a general class of coupled bead-spring chain models with finitely extensible nonlinear elastic (FENE) type spring potentials for nonhomogeneous incompressible dilute polymeric fluids in a bounded domain in $mathbb{R}^d$, $d=2$ or $3$. The class of models under consideration involves the Navier--Stokes system with variable density, where the viscosity coefficient depends on both the density and the polymer number density, coupled to a Fokker--Planck equation with a density-dependent drag coefficient. The proof is based on combining a truncation of the probability density function with a two-stage Galerkin approximation and weak compactness and compensated compactness techniques to pass to the limits in the sequence of Galerkin approximations and in the truncation level.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87628517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Flocking of the Cucker-Smale and Motsch-Tadmor models on general weighted digraphs via a probabilistic method 广义加权有向图上cucker - small和Motsch-Tadmor模型的概率聚类
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2022-02-10 DOI: 10.3934/krm.2022040
Adrien Cotil
{"title":"Flocking of the Cucker-Smale and Motsch-Tadmor models on general weighted digraphs via a probabilistic method","authors":"Adrien Cotil","doi":"10.3934/krm.2022040","DOIUrl":"https://doi.org/10.3934/krm.2022040","url":null,"abstract":". In this paper, we discuss the flocking phenomenon for the Cucker-Smale and Motsch-Tadmor models in continuous time on a general oriented and weighted graph with a general communication function. We present a new approach for studying this problem based on a probabilistic interpretation of the solutions. We provide flocking results under four assumptions on the interaction matrix and we highlight how they relate to the convergence in total variation of a certain Markov jump process. Indeed, we refine previous results on the minimal case where the graph admits a unique closed communication class. Considering the two particular cases where the adjacency matrix is scrambling or where it admits a positive reversible measure, we improve the flocking condition obtained for the minimal case. In the last case, we characterise the asymptotic speed. We also study the hierarchical leadership case where we give a new general flocking condition which allows to deal with the case ψ ( r ) ∝ (1 + r 2 ) − β/ 2 and β ≥ 1. For the Motsch-Tadmor model under the hierarchical leadership assumption, we exhibit a case where the flocking phenomenon occurs regardless of the initial conditions and the communication function, in particular even if β ≥ 1.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88924308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic growth and decay of two-dimensional symmetric plasmas 二维对称等离子体的渐近生长和衰减
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2022-02-08 DOI: 10.3934/krm.2023015
Jonathan Ben-Artzi, Baptiste Morisse, S. Pankavich
{"title":"Asymptotic growth and decay of two-dimensional symmetric plasmas","authors":"Jonathan Ben-Artzi, Baptiste Morisse, S. Pankavich","doi":"10.3934/krm.2023015","DOIUrl":"https://doi.org/10.3934/krm.2023015","url":null,"abstract":"We study the large time behavior of classical solutions to the two-dimensional Vlasov-Poisson (VP) and relativistic Vlasov-Poisson (RVP) systems launched by radially-symmetric initial data with compact support. In particular, we prove that particle positions and momenta grow unbounded as $t to infty$ and obtain sharp rates on the maximal values of these quantities on the support of the distribution function for each system. Furthermore, we establish nearly sharp rates of decay for the associated electric field, as well as upper and lower bounds on the decay rate of the charge density in the large time limit. We prove that, unlike (VP) in higher dimensions, smooth solutions do not scatter to their free-streaming profiles as $t to infty$ because nonlinear, long-range field interactions dominate the behavior of characteristics due to the exchange of energy from the potential to the kinetic term. In this way, the system may\"forget\"any previous configuration of particles.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79330734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A simple proof of non-explosion for measure solutions of the Keller-Segel equation Keller-Segel方程测度解的非爆炸性的一个简单证明
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2022-02-07 DOI: 10.3934/krm.2022026
N. Fournier, Yoan Tardy
{"title":"A simple proof of non-explosion for measure solutions of the Keller-Segel equation","authors":"N. Fournier, Yoan Tardy","doi":"10.3934/krm.2022026","DOIUrl":"https://doi.org/10.3934/krm.2022026","url":null,"abstract":"<p style='text-indent:20px;'>We give a simple proof, relying on a <i>two-particles</i> moment computation, that there exists a global weak solution to the <inline-formula><tex-math id=\"M1\">begin{document}$ 2 $end{document}</tex-math></inline-formula>-dimensional parabolic-elliptic Keller-Segel equation when starting from any initial measure <inline-formula><tex-math id=\"M2\">begin{document}$ f_0 $end{document}</tex-math></inline-formula> such that <inline-formula><tex-math id=\"M3\">begin{document}$ f_0( {mathbb{R}}^2)< 8 pi $end{document}</tex-math></inline-formula>.</p>","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87884794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Well-posedness and singularity formation for Vlasov–Riesz system Vlasov-Riesz系统的适位性和奇点形成
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2022-01-31 DOI: 10.3934/krm.2023030
Young-Pil Choi, In-Jee Jeong
{"title":"Well-posedness and singularity formation for Vlasov–Riesz system","authors":"Young-Pil Choi, In-Jee Jeong","doi":"10.3934/krm.2023030","DOIUrl":"https://doi.org/10.3934/krm.2023030","url":null,"abstract":"We investigate the Cauchy problem for the Vlasov--Riesz system, which is a Vlasov equation featuring an interaction potential generalizing previously studied cases, including the Coulomb $Phi = (-Delta)^{-1}rho$, Manev $(-Delta)^{-1} + (-Delta)^{-frac12}$, and pure Manev $(-Delta)^{-frac12}$ potentials. For the first time, we extend the local theory of classical solutions to potentials more singular than that for the Manev. Then, we obtain finite-time singularity formation for solutions with various attractive interaction potentials, extending the well-known blow-up result of Horst for attractive Vlasov--Poisson for $dge4$. Our local well-posedness and singularity formation results extend to cases when linear diffusion and damping in velocity are present.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82244387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
A stochastic particle system approximating the BGK equation 近似BGK方程的随机粒子系统
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2022-01-05 DOI: 10.3934/krm.2022029
P. Buttà, M. Pulvirenti
{"title":"A stochastic particle system approximating the BGK equation","authors":"P. Buttà, M. Pulvirenti","doi":"10.3934/krm.2022029","DOIUrl":"https://doi.org/10.3934/krm.2022029","url":null,"abstract":"<p style='text-indent:20px;'>We consider a stochastic <inline-formula><tex-math id=\"M1\">begin{document}$ N $end{document}</tex-math></inline-formula>-particle system on a torus in which each particle moving freely can instantaneously thermalize according to the particle configuration at that instant. Following [<xref ref-type=\"bibr\" rid=\"b2\">2</xref>], we show that the propagation of chaos does hold and that the one-particle distribution converges to the solution of the BGK equation. The improvement with respect to [<xref ref-type=\"bibr\" rid=\"b2\">2</xref>] consists in the fact that here, as suggested by physical considerations, the thermalizing transition is driven only by the restriction of the particle configuration in a small neighborhood of the jumping particle. In other words, the Maxwellian distribution of the outgoing particle is computed via the empirical hydrodynamical fields associated to the fraction of particles sufficiently close to the test particle and not, as in [<xref ref-type=\"bibr\" rid=\"b2\">2</xref>], via the whole particle configuration.</p>","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86023433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Linearized Boltzmann collision operator: II. Polyatomic molecules modeled by a continuous internal energy variable 线性化玻尔兹曼碰撞算子:由连续内能变量模拟的多原子分子
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2022-01-04 DOI: 10.3934/krm.2023009
Niclas Bernhoff
{"title":"Linearized Boltzmann collision operator: II. Polyatomic molecules modeled by a continuous internal energy variable","authors":"Niclas Bernhoff","doi":"10.3934/krm.2023009","DOIUrl":"https://doi.org/10.3934/krm.2023009","url":null,"abstract":"The linearized collision operator of the Boltzmann equation for single species can be written as a sum of a positive multiplication operator, the collision frequency, and a compact integral operator. This classical result has more recently, been extended to multi-component mixtures and polyatomic single species with the polyatomicity modeled by a discrete internal energy variable. In this work we prove compactness of the integral operator for polyatomic single species, with the polyatomicity modeled by a continuous internal energy variable, and the number of internal degrees of freedom greater or equal to two. The terms of the integral operator are shown to be, or be the uniform limit of, Hilbert-Schmidt integral operators. Self-adjointness of the linearized collision operator follows. Coercivity of the collision frequency are shown for hard-sphere like and hard potential with cut-off like models, implying Fredholmness of the linearized collision operator.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74517260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
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