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Kinetic and Related Models最新文献

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A moment closure based on a projection on the boundary of the realizability domain: Extension and analysis 基于可实现域边界投影的矩闭包:推广与分析
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2022-01-01 DOI: 10.3934/krm.2022014
T. Pichard
{"title":"A moment closure based on a projection on the boundary of the realizability domain: Extension and analysis","authors":"T. Pichard","doi":"10.3934/krm.2022014","DOIUrl":"https://doi.org/10.3934/krm.2022014","url":null,"abstract":"A closure relation for moments equations in kinetic theory was recently introduced in [38], based on the study of the geometry of the set of moments. This relation was constructed from a projection of a moment vector toward the boundary of the set of moments and corresponds to approximating the underlying kinetic distribution as a sum of a chosen equilibrium distribution plus a sum of purely anisotropic Dirac distributions.The present work generalizes this construction for kinetic equations involving unbounded velocities, i.e. to the Hamburger problem, and provides a deeper analysis of the resulting moment system. Especially, we provide representation results for moment vectors along the boundary of the moment set that implies the well-definition of the model. And the resulting moment model is shown to be weakly hyperbolic with peculiar properties of hyperbolicity and entropy of two subsystems, corresponding respectively to the equilibrium and to the purely anisotropic parts of the underlying kinetic distribution.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":"25 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79764078","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
Global existence of strong solutions to the kinetic Cucker-Smale model coupled with the two dimensional incompressible Navier-Stokes equations 二维不可压缩Navier-Stokes方程耦合动力学cucker - small模型强解的整体存在性
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2022-01-01 DOI: 10.3934/krm.2022023
Chunyin Jin
{"title":"Global existence of strong solutions to the kinetic Cucker-Smale model coupled with the two dimensional incompressible Navier-Stokes equations","authors":"Chunyin Jin","doi":"10.3934/krm.2022023","DOIUrl":"https://doi.org/10.3934/krm.2022023","url":null,"abstract":"In this paper, we investigate existence of global-in-time strong solutions to the Cauchy problem of the kinetic Cucker–Smale model coupled with the incompressible Navier–Stokes equations in the two dimensional space. By introducing a weighted Sobolev space and using the maximal regularity estimate on the linear non-stationary Stokes equations, we present a complete analysis on existence of global-in-time strong solutions to the coupled model, without any smallness assumptions on initial data.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":"285 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75422347","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
Cucker-Smale model with finite speed of information propagation: Well-posedness, flocking and mean-field limit 有限信息传播速度的cucker -小模型:适定性、群集和平均场极限
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2021-12-23 DOI: 10.3934/krm.2022033
J. Haskovec
{"title":"Cucker-Smale model with finite speed of information propagation: Well-posedness, flocking and mean-field limit","authors":"J. Haskovec","doi":"10.3934/krm.2022033","DOIUrl":"https://doi.org/10.3934/krm.2022033","url":null,"abstract":"<p style='text-indent:20px;'>We study a variant of the Cucker-Smale model where information between agents propagates with a finite speed <inline-formula><tex-math id=\"M1\">begin{document}$ {{mathfrak{c}}}>0 $end{document}</tex-math></inline-formula>. This leads to a system of functional differential equations with state-dependent delay. We prove that, if initially the agents travel slower than <inline-formula><tex-math id=\"M2\">begin{document}$ {{mathfrak{c}}} $end{document}</tex-math></inline-formula>, then the discrete model admits unique global solutions. Moreover, under a generic assumption on the influence function, we show that there exists a critical information propagation speed <inline-formula><tex-math id=\"M3\">begin{document}$ {{{{mathfrak{c}}}^ast}}>0 $end{document}</tex-math></inline-formula> such that if <inline-formula><tex-math id=\"M4\">begin{document}$ {{mathfrak{c}}}geq{{{{mathfrak{c}}}^ast}} $end{document}</tex-math></inline-formula>, the system exhibits asymptotic flocking in the sense of the classical definition of Cucker and Smale. For constant initial datum the value of <inline-formula><tex-math id=\"M5\">begin{document}$ {{{{mathfrak{c}}}^ast}} $end{document}</tex-math></inline-formula> is explicitly calculable. Finally, we derive a mean-field limit of the discrete system, which is formulated in terms of probability measures on the space of time-dependent trajectories. We show global well-posedness of the mean-field problem and argue that it does not admit a description in terms of the classical Fokker-Planck equation.</p>","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":"116 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77972240","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
On $ C^{2} $ solution of the free-transport equation in a disk 圆盘自由输运方程的$ C^{2} $解
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2021-12-03 DOI: 10.3934/krm.2022031
G. Ko, Donghyung Lee
{"title":"On $ C^{2} $ solution of the free-transport equation in a disk","authors":"G. Ko, Donghyung Lee","doi":"10.3934/krm.2022031","DOIUrl":"https://doi.org/10.3934/krm.2022031","url":null,"abstract":"<p style='text-indent:20px;'>The free transport operator of probability density function <inline-formula><tex-math id=\"M2\">begin{document}$ f(t, x, v) $end{document}</tex-math></inline-formula> is one the most fundamental operator which is widely used in many areas of PDE theory including kinetic theory, in particular. When it comes to general boundary problems in kinetic theory, however, it is well-known that high order regularity is very hard to obtain in general. In this paper, we study the free transport equation in a disk with the specular reflection boundary condition. We obtain initial-boundary compatibility conditions for <inline-formula><tex-math id=\"M3\">begin{document}$ C^{1}_{t, x, v} $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M4\">begin{document}$ C^{2}_{t, x, v} $end{document}</tex-math></inline-formula> regularity of the solution. We also provide regularity estimates.</p>","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":"74 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77111579","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
The Boltzmann-Grad limit for the Lorentz gas with a Poisson distribution of obstacles 障碍泊松分布的洛伦兹气体的玻尔兹曼-格拉德极限
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2021-11-30 DOI: 10.3934/krm.2022001
F. Golse
{"title":"The Boltzmann-Grad limit for the Lorentz gas with a Poisson distribution of obstacles","authors":"F. Golse","doi":"10.3934/krm.2022001","DOIUrl":"https://doi.org/10.3934/krm.2022001","url":null,"abstract":"<p style='text-indent:20px;'>In this note, we propose a slightly different proof of Gallavotti's theorem [\"Statistical Mechanics: A Short Treatise\", Springer, 1999, pp. 48-55] on the derivation of the linear Boltzmann equation for the Lorentz gas with a Poisson distribution of obstacles in the Boltzmann-Grad limit.</p>","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":"95 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79548176","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
The inviscid limit for the 2D Navier-Stokes equations in bounded domains 二维Navier-Stokes方程在有界区域的无粘极限
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2021-11-29 DOI: 10.3934/krm.2022004
C. Bardos, Trinh T. Nguyen, Toan T. Nguyen, E. Titi
{"title":"The inviscid limit for the 2D Navier-Stokes equations in bounded domains","authors":"C. Bardos, Trinh T. Nguyen, Toan T. Nguyen, E. Titi","doi":"10.3934/krm.2022004","DOIUrl":"https://doi.org/10.3934/krm.2022004","url":null,"abstract":"We prove the inviscid limit for the incompressible Navier-Stokes equations for data that are analytic only near the boundary in a general two-dimensional bounded domain. Our proof is direct, using the vorticity formulation with a nonlocal boundary condition, the explicit semigroup of the linear Stokes problem near the flatten boundary, and the standard wellposedness theory of Navier-Stokes equations in Sobolev spaces away from the boundary.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":"175 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76964311","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: 8
Kinetic Fokker-Planck and Landau equations with specular reflection boundary condition 具有镜面反射边界条件的动力学Fokker-Planck和Landau方程
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2021-11-18 DOI: 10.3934/krm.2022003
Hongjie Dong, Yan Guo, Timur Yastrzhembskiy
{"title":"Kinetic Fokker-Planck and Landau equations with specular reflection boundary condition","authors":"Hongjie Dong, Yan Guo, Timur Yastrzhembskiy","doi":"10.3934/krm.2022003","DOIUrl":"https://doi.org/10.3934/krm.2022003","url":null,"abstract":"<p style='text-indent:20px;'>We establish existence of finite energy weak solutions to the kinetic Fokker-Planck equation and the linear Landau equation near Maxwellian, in the presence of specular reflection boundary condition for general domains. Moreover, by using a method of reflection and the <inline-formula><tex-math id=\"M1\">begin{document}$ S_p $end{document}</tex-math></inline-formula> estimate of [<xref ref-type=\"bibr\" rid=\"b7\">7</xref>], we prove regularity in the kinetic Sobolev spaces <inline-formula><tex-math id=\"M2\">begin{document}$ S_p $end{document}</tex-math></inline-formula> and anisotropic Hölder spaces for such weak solutions. Such <inline-formula><tex-math id=\"M3\">begin{document}$ S_p $end{document}</tex-math></inline-formula> regularity leads to the uniqueness of weak solutions.</p>","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":"24 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82769968","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
A kinetic chemotaxis model with internal states and temporal sensing 具有内部状态和时间感知的动力学趋化模型
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2021-11-17 DOI: 10.3934/krm.2021043
Zhian Wang
{"title":"A kinetic chemotaxis model with internal states and temporal sensing","authors":"Zhian Wang","doi":"10.3934/krm.2021043","DOIUrl":"https://doi.org/10.3934/krm.2021043","url":null,"abstract":"<p style='text-indent:20px;'>By employing the Fourier transform to derive key <i>a priori</i> estimates for the temporal gradient of the chemical signal, we establish the existence of global solutions and hydrodynamic limit of a chemotactic kinetic model with internal states and temporal gradient in one dimension, which is a system of two transport equations coupled to a parabolic equation proposed in [<xref ref-type=\"bibr\" rid=\"b4\">4</xref>].</p>","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":"23 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74833194","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
Magnetic confinement for the 2D axisymmetric relativistic Vlasov-Maxwell system in an annulus 环空中二维轴对称相对论Vlasov-Maxwell系统的磁约束
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2021-11-08 DOI: 10.3934/krm.2021039
Jin Woo Jang, Robert M. Strain, T. Wong
{"title":"Magnetic confinement for the 2D axisymmetric relativistic Vlasov-Maxwell system in an annulus","authors":"Jin Woo Jang, Robert M. Strain, T. Wong","doi":"10.3934/krm.2021039","DOIUrl":"https://doi.org/10.3934/krm.2021039","url":null,"abstract":"Although the nuclear fusion process has received a great deal of attention in recent years, the amount of mathematical analysis that supports the stability of the system seems to be relatively insufficient. This paper deals with the mathematical analysis of the magnetic confinement of the plasma via kinetic equations. We prove the global wellposedness of the Vlasov-Maxwell system in a two-dimensional annulus when a huge (but finite-in-time) external magnetic potential is imposed near the boundary. We assume that the solution is axisymmetric. The authors hope that this work is a step towards a more generalized work on the three-dimensional Tokamak structure. The highlight of this work is the physical assumptions on the external magnetic potential well which remains finite within a finite time interval and from that, we prove that the plasma never touches the boundary. In addition, we provide a sufficient condition on the magnitude of the external magnetic potential to guarantee that the plasma is confined in an annulus of the desired thickness which is slightly larger than the initial support. Our method uses the cylindrical coordinate forms of the Vlasov-Maxwell system.","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":"14 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82411038","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: 2
Glassey-Strauss representation of Vlasov-Maxwell systems in a Half Space 半空间中Vlasov-Maxwell系统的Glassey-Strauss表示
IF 1 4区 数学
Kinetic and Related Models Pub Date : 2021-10-20 DOI: 10.3934/krm.2021034
Yunbai Cao, Chanwoo Kim
{"title":"Glassey-Strauss representation of Vlasov-Maxwell systems in a Half Space","authors":"Yunbai Cao, Chanwoo Kim","doi":"10.3934/krm.2021034","DOIUrl":"https://doi.org/10.3934/krm.2021034","url":null,"abstract":"<p style='text-indent:20px;'>Following closely the classical works [<xref ref-type=\"bibr\" rid=\"b5\">5</xref>]-[<xref ref-type=\"bibr\" rid=\"b7\">7</xref>] by Glassey, Strauss, and Schaeffer, we present a version of the Glassey-Strauss representation for the Vlasov-Maxwell systems in a 3D half space when the boundary is the perfect conductor.</p>","PeriodicalId":49942,"journal":{"name":"Kinetic and Related Models","volume":"383 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76445350","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: 2
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