Related papers: Global existence for the relativistic Vlasov-Poiss…
We prove global existence of strong solutions for the Vlasov-Poisson system in a convex bounded domain in the plasma physics case assuming homogeneous Dirichlet boundary conditions for the electric potential and the specular reflection…
In this paper we prove global existence for solutions of the Vlasov-Poisson system in convex bounded domains with specular boundary conditions and with a prescribed outward electrical field at the boundary.
In this paper we prove global existence of classical solutions to the Vlasov-Poisson and the ionic Vlasov-Poisson models in bounded domains. On the boundary, we consider the specular reflection boundary condition for the Vlasov equation and…
When dilute charged particles are confined in a bounded domain, boundary effects are crucial in the global dynamics. We construct a unique global-in-time solution to the Vlasov-Poisson-Boltzmann system in convex domains with the diffuse…
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…
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…
For a class of arbitrary large initial data with radial symmetry or cylindrical symmetry, we prove the existence of global solutions for the $3D$ relativistic Vlasov-Poisson system for the plasma physics case. The compact support assumption…
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…
In this paper, we establish the global existence of Lagrangian solutions to the ionic Vlasov--Poisson system under mild integrability assumptions on the initial data. Our approach involves proving the well-posedness of the…
The purpose of this paper is twofold. In the first part, we provide a new proof of the global existence of the solutions to the Vlasov-Maxwell system with a small initial distribution function. Our approach relies on vector field methods,…
In a recent paper Calogero and Alcantara derived a Lorentz-invariant Fokker-Planck equation, which corresponds to the evolution of a particle distribution associated with relativistic Brownian Motion. We study the "one and one-half"…
The global solutions in critical spaces to the multi-dimensional compressible viscoelastic flows are considered. The global existence of the Cauchy problem with initial data close to an equilibrium state is established in Besov spaces.…
Consider the relativistic Vlasov-Maxwell-Boltzmann system describing the dynamics of an electron gas in the presence of a fixed ion background. Thanks to recent works \cite{Germain-Masmoudi-ASENS-2014, Guo-Ionescu-Pausader-JMP-2014} and…
We study the Lagrangian structure of relativistic Vlasov systems, such as the relativistic Vlasov-Poisson and the relativistic quasi-eletrostatic limit of Vlasov-Maxwell equations. We show that renormalized solutions of these systems are…
We consider the two-dimensional Vlasov-Poisson system to model a two-component plasma whose distribution function is constant with respect to the third space dimension. First, we show how this two-dimensional Vlasov-Poisson system can be…
We show that the Nernst-Planck-Euler system, which models ionic electrodiffusion in fluids, has global strong solutions for arbitrarily large data in the two dimensional bounded domains. The assumption on species is either there are two…
In this work, we study the global existence of solutions for a class of semilinear nonlocal reaction-diffusion systems with $m$ components on a bounded domain $\Omega$ in $\mathbb{R}^n$ with smooth boundary. The initial data is assumed to…
In this paper, we are concerned with the local and global existence for the stochastic Prandtl equation in two and three dimensions, which governs the velocity field inside the boundary layer that appears in the inviscid limit of the…
A collisionless plasma is modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge - dependant upon only velocity - is assumed. The situation in which mobile negative ions balance the positive…
The relativistic Vlasov-Maxwell system is a kinetic model for collisionless plasmas. For the two-dimensional model, global well-posedness of this model is known and was proven by deriving global bounds on the momentum support of the…