English
Related papers

Related papers: The non-cutoff Vlasov-Poisson-Boltzmann system wit…

200 papers

The Cauchy problem for the Boltzmann equation with soft potential, in the framework of small perturbation of an equilibrium state, has been studied in many spaces. The method of strongly continuous semigroup has been applied by…

Analysis of PDEs · Mathematics 2024-02-08 Dingqun Deng

In this paper, we propose a new convex approach to stability analysis of nonlinear systems with polynomial vector fields. First, we consider an arbitrary convex polytope that contains the equilibrium in its interior. Then, we decompose the…

Optimization and Control · Mathematics 2014-11-24 Reza Kamyar , Chaitanya Murti , Matthew Peet

The ionic Vlasov-Poisson-Boltzmann system is a fundamental model in dilute collisional plasmas. In this work, we study the compressible ionic Euler-Poisson limit of the ionic Vlasov-Poisson-Boltzmann system for the full range of cutoff…

Analysis of PDEs · Mathematics 2026-01-14 Qin Ye , Fujun Zhou , Weijun Wu

For the Landau-Poisson system with Coulomb interaction in $\R^3_x$, we prove the global existence, uniqueness, and large time convergence rates to the Maxwellian equilibrium for solutions which start out sufficiently close.

Analysis of PDEs · Mathematics 2016-02-22 Robert M. Strain , Keya Zhu

Lattice Boltzmann methods are usually derived under the assumption of isotropy. In this work, we present a derivation of a Lattice Boltzmann method for anisotropic fluid flow. Starting from an anisotropic equilibrium distribution, we show a…

Fluid Dynamics · Physics 2026-05-27 Benjamin Kellers , Julius Weinmiller , Arnulf Latz , Timo Danner

In this paper, we consider the global well-posedness to the non-cutoff Boltzmann equation with soft potential in the $L^\infty$ setting. We show that when the initial data is close to equilibrium and the perturbation is small in $L^2 \cap…

Analysis of PDEs · Mathematics 2022-10-19 Chuqi Cao

Efficient and accurate numerical approximation of the full Boltzmann equation has been a longstanding challenging problem in kinetic theory. This is mainly due to the high dimensionality of the problem and the complicated collision…

Numerical Analysis · Mathematics 2021-12-07 Jingwei Hu , Yubo Wang

We consider a 1D-2V Vlasov-Fokker-Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we…

Plasma Physics · Physics 2018-05-09 William T. Taitano , Luis Chacon , Andrei N. Simakov

We prove global existence of weak solutions for a version of one velocity Baer-Nunziato system with dissipation describing a mixture of two non interacting viscous compressible fluids in a piecewise regular Lipschitz domain with general…

Analysis of PDEs · Mathematics 2021-05-12 Stanislav Kracmar , Young-Sam Kwon , Sarka Necasova , Antonin Novotny

We consider the compressible Poisson-Nernst-Planck-Navier-Stokes (PNPNS) system of equations, governing the transport of charged particles under the influence of the self-consistent electrostatic potential, in a three-dimensional bounded…

Analysis of PDEs · Mathematics 2024-10-03 Daniel Marroquin , Dehua Wang

We construct a novel class of exact solutions to the Boltzmann equation, in both its classical and quantum formulation, for arbitrary collision laws. When the system is subjected to a specific external forcing, the precise form of which is…

Statistical Mechanics · Physics 2015-06-19 D. Guéry-Odelin , J. G. Muga , M. J. Ruiz-Montero , E. Trizac

This paper presents a grid-free simulation algorithm for the fully three-dimensional Vlasov--Poisson system for collisionless electron plasmas. We employ a standard particle method for the numerical approximation of the distribution…

Numerical Analysis · Mathematics 2020-03-06 Torsten Keßler , Sergej Rjasanow , Steffen Weißer

Using relativistic kinetic theory, we study spherically symmetric, static equilibrium configurations of a collisionless Maxwell-Boltzmann gas with non-standard self-interactions, modelled by an effective one--particle force. The resulting…

Astrophysics · Physics 2009-11-10 Alexander Balakin , Roberto A. Sussman , Winfried Zimdahl

This paper establishes the global existence of solutions for a class of wave-Klein-Gordon coupled systems with specific nonlinearities in 3+1-dimensional Minkowski spacetime. The study demonstrates that imposing certain constraints on the…

Analysis of PDEs · Mathematics 2026-04-21 Yue Ma , Weidong Zhang

The quantum version of the Boltzmann transport equation (Wigner-Boltzmann equation) is a quite useful tool to investigate the effects of energy dissipation in quantum systems. Numerical approaches uses to be employed in order to stablish a…

Statistical Mechanics · Physics 2017-09-19 A. R. Fernandes Nt. , L. F. Santos

Computational modeling and simulation of fluid-structure interactions constitute a fundamental cornerstone for advancing aerospace engineering endeavors. This paper addresses the notion and implementation of the immersed boundary method for…

Computational Physics · Physics 2025-12-24 Longqing Ge , Qingdong Cai , Yonghao Zhang , Tianbai Xiao

This article proves the regularity for the Boltzmann equation without angular cutoff with hard potential. By sharpening the coercivity and upper bound estimate on the collision operator, analyzing the Poisson bracket between the transport…

Analysis of PDEs · Mathematics 2022-08-10 Dingqun Deng

This work proves the global stability of the Boltzmann equation (1872) with the physical collision kernels derived by Maxwell in 1866 for the full range of inverse-power intermolecular potentials, $r^{-(p-1)}$ with $p>2$, for initial…

Analysis of PDEs · Mathematics 2011-04-05 Philip T. Gressman , Robert M. Strain

The paper considers a linear system of Boltzmann transport equations modelling the evolution of three species of particles, photons, electrons and positrons. The system is coupled because of the collision term (an integral operator). The…

Optimization and Control · Mathematics 2017-02-02 Jouko Tervo , Petri Kokkonen

We study the global existence and uniqueness of weak solutions to kinetic Kolmogorov-Vicsek models that can be considered a non-local non-linear Fokker-Planck type equation describing the dynamics of individuals with orientational…

Analysis of PDEs · Mathematics 2016-05-02 Irene M. Gamba , Moon-Jin Kang