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We construct a unique global-in-time solution to the two species Vlasov-Poisson-Boltzmann system in convex domains with the diffuse boundary condition, which can be viewed as one of the ideal scattering boundary model. The construction…

Analysis of PDEs · Mathematics 2019-06-07 Yunbai Cao

In this paper, we consider the dispersive limit of the Euler-Poisson system for ion-acoustic waves. We establish that under the Gardner-Morikawa type transformations, the solutions of the Euler-Poisson system converge globally to the…

Mathematical Physics · Physics 2013-04-30 Xueke Pu

The motion of a fully ionized plasma of electrons and ions is generally governed by the Vlasov-Maxwell-Landau system. We prove the global existence of solutions near Maxwellians to the Cauchy problem of the system for the long-range…

Analysis of PDEs · Mathematics 2012-05-25 Renjun Duan

The Euler-Maxwell system describes the evolution of a plasma when the collisions are important enough that each species is in a hydrodynamic equilibrium. In this paper we prove global existence of small solutions to this system set in the…

Analysis of PDEs · Mathematics 2011-07-11 Pierre Germain , Nader Masmoudi

We prove asymptotic stability of the Poisson homogeneous equilibrium among solutions of the Vlassov-Poisson system in the Euclidean space $\mathbb{R}^3$. More precisely, we show that small, smooth, and localized perturbations of the Poisson…

Analysis of PDEs · Mathematics 2024-01-30 Alexandru Ionescu , Benoit Pausader , Xuecheng Wang , Klaus Widmayer

Boundary effects are crucial for dynamics of dilute charged gases governed by the Vlasov-Poisson-Boltzmann (VPB) system. In this paper, we study the existence and regularity of solutions to the VPB system with soft potential in a bounded…

Analysis of PDEs · Mathematics 2021-11-18 Fucai Li , Yichun Wang

The classical Euler--Poinsot case of the rigid body dynamics admits a class of simple but non-trivial integrable generalizations, which modify the Poisson equations describing the motion of the body in space. These generalizations possess…

Exactly Solvable and Integrable Systems · Physics 2015-06-15 Yuri N. Fedorov , Andrzej J. Maciejewski , Maria Przybylska

We investigate rescaling transformations for the Vlasov-Poisson and Euler-Poisson systems and derive in the plasma physics case Lyapunov functionals which can be used to analyze dispersion effects. The method is also used for studying the…

Analysis of PDEs · Mathematics 2007-05-23 Jean Dolbeault , Gerhard Rein

We establish both global existence and decay properties for solutions with small data for a general class of coupled system of tensorial quasilinear hyperbolic wave equations in three space dimensions, that covers the dynamical Einstein…

Analysis of PDEs · Mathematics 2026-03-03 Sari Ghanem

We consider the one-dimensional ions dynamics in weakly collisional plasmas governed by the Vlasov-Poisson-Landau system under the Boltzmann relation with the small collision frequency $\nu>0$. It is observed in physical experiments that…

Analysis of PDEs · Mathematics 2025-07-01 Renjun Duan , Zongguang Li , Dongcheng Yang , Tong Yang

We study the formation of singularity for the Euler-Poisson system equipped with the Boltzmann relation, which describes the dynamics of ions in an electrostatic plasma. In general, it is known that smooth solutions to nonlinear hyperbolic…

Analysis of PDEs · Mathematics 2022-06-07 Junsik Bae , Junho Choi , Bongsuk Kwon

Three-dimensional two-layer incompressible Euler fluids are studied from a Hamiltonian perspective. A natural Hamiltonian structure for the effective 2D model described by the interface-value of the field variables is obtained by means of a…

Mathematical Physics · Physics 2026-04-27 R. Camassa , G. Falqui , G. Ortenzi , M. Pedroni , E. Sforza

This work concerns the Vlasov-Poisson-Boltzmann system without angular cutoff and Vlasov-Poisson-Landau system including Coulomb interaction in bounded domain, namely union of cubes. We establish the global stability, exponential large-time…

Analysis of PDEs · Mathematics 2022-08-24 Dingqun Deng

The study of flows over an obstacle is one of the fundamental problems in fluids. In this paper we establish the global validity of the diffusive limit for the Boltzmann equations to the Navier-Stokes-Fourier system in an exterior domain.…

Analysis of PDEs · Mathematics 2025-01-17 Junhwa Jung

In this paper, we establish the global in time hydrodynamic limit of Boltzmann equation to the planar rarefaction wave of compressible Euler system in three dimensional space $x\in\mathbb{R}^3$ for general collision kernels. Our approch is…

Analysis of PDEs · Mathematics 2019-10-18 Guanfa Wang , Yong Wang , Jiawei Zhou

The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. In the 3D case Guo first constructed a global smooth irrotational solution…

Mathematical Physics · Physics 2013-11-25 Dong Li , Yifei Wu

In this paper we study the regularity of the non-cutoff Vlasov-Poisson-Boltzmann system for plasma particles of two species in the whole space $\mathbb{R}^3$ with hard potential. The existence of global-in-time nearby Maxwellian solutions…

Analysis of PDEs · Mathematics 2021-09-22 Dingqun Deng

In some inertial confinement fusion hohlraum designs, the inside plasma is not sufficiently collisional to be satisfactorily described by the Euler equations implemented in hydrodynamic simulation codes, particularly in converging regions…

Plasma Physics · Physics 2021-11-30 Olivier Larroche

In this work, we deal with the Vlasov-Poisson system in smooth physical domains with specular boundary condition, under mild integrability assumptions, and $d \ge 3$. We show that the Lagrangian and Eulerian descriptions of the system are…

Analysis of PDEs · Mathematics 2018-09-26 Xavier Fernández-Real

Here we investigate global strong solutions for a class of partially dissipative hyperbolic systems in the framework of critical homogeneous Besov spaces. Our primary goal is to extend the analysis of our previous paper [10] to a functional…

Analysis of PDEs · Mathematics 2022-01-19 Timothée Crin-Barat , Raphaël Danchin