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In this paper, we consider the full compressible, viscous, non-resistive MHD system under the assumption that the fluids move on a plane while the magnetic field is oriented vertically. Within the framework of Besov spaces, by introducing…

Analysis of PDEs · Mathematics 2024-08-15 Xiaoping Zhai , Shunhang Zhang

We study a positively charged Vlasov-Poisson plasma in which N negative point charges are immersed. The attractiveness of the system forces us to consider a possibly unbounded plasma density near the charges. We prove the existence of a…

Analysis of PDEs · Mathematics 2011-06-29 Silvia Caprino , Carlo Marchioro , Evelyne Miot , Mario Pulvirenti

The goal of this article is twofold. First, we investigate the linearized Vlasov-Poisson system around a family of spatially homogeneous equilibria in $\mathbb{R}^3$ (the unconfined setting). Our analysis follows classical strategies from…

Analysis of PDEs · Mathematics 2023-09-20 Alexandru D. Ionescu , Benoit Pausader , Xuecheng Wang , Klaus Widmayer

A collisionless plasma is modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge, which is independent of time and space, is assumed. The situation in which mobile negative ions balance the…

Analysis of PDEs · Mathematics 2015-05-14 Stephen Pankavich

In this paper, we consider the three-dimensional full compressible viscous non-resistive MHD system. Global well-posedness is proved for an initial-boundary value problem around a strong background magnetic field. It is also shown that the…

Analysis of PDEs · Mathematics 2022-03-09 Yang Li

In this paper, we consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in…

Analysis of PDEs · Mathematics 2023-07-19 Jinrui Huang , Shijin Ding

We are concerned with the well-posedness of the density-dependent incompressible viscoelastic fluid system. By Schauder-Tychonoff fixed point argument, when $\|{1}/{\rho_0}-1\|_{\dot{B}_{p,1}^{{N}/{p}}}$ is small, local well-posedness is…

Analysis of PDEs · Mathematics 2011-05-25 Huazhao Xie , Yunxia Fu

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

This paper aims to establish the global existence of strong solutions to a non-isothermal ideal gas model. We first show global well-posedness in the Sobolev space $H^2(\mathbb{R}^3)$ by using energy estimates. We then prove the global…

Analysis of PDEs · Mathematics 2022-03-17 Bin Han , Ning-An Lai , Andrei Tarfulea

We consider a special case of the three dimensional Vlasov-Poisson system where the particles are restricted to a plane, a situation that is used in astrophysics to model extremely flattened galaxies. We prove the existence of steady states…

Mathematical Physics · Physics 2009-10-31 Gerhard Rein

In this paper, we prove the global existence of solutions to the relativistic Vlasov-Poisson system for general initial data in convex bounded domains of two space dimensions, assuming the specular reflection boundary conditions for the…

Analysis of PDEs · Mathematics 2025-11-11 Yanmin Mu , Dehua Wang

We construct the global unique solution near a global Maxwellian to the Vlasov-Poisson-Landau system in the whole space. The total density of two species of particles decays at the optimal algebraic rates as the Landau equation in the whole…

Analysis of PDEs · Mathematics 2015-09-29 Yanjin Wang

In this short note, we provide the well-posedness for an hyperbolic-hyperbolic-elliptic system of PDEs describing the motion of collision free-plasma in magnetic fields. The proof combines a pointwise estimate together with a bootstrap type…

Analysis of PDEs · Mathematics 2023-09-14 Diego Alonso-Orán , Rafael Granero-Belinchón

We prove the global-in-time existence of large-data finite-energy weak solutions to an incompressible hybrid Vlasov-magnetohydrodynamic model in three space dimensions. The model couples three essential ingredients of magnetized plasmas: a…

Analysis of PDEs · Mathematics 2017-07-05 Bin Cheng , Endre Süli , Cesare Tronci

This article focuses on the Vlasov-Poisson system with point charges in bounded convex domains, accounting the interactions of point charges with the self-consistent electric field and the boundary, which were not addressed in the previous…

Analysis of PDEs · Mathematics 2026-04-14 Jingpeng Wu

The mathematical description of laboratory fusion plasmas produced in Tokamaks is still challenging. Complete models for electrons and ions, as Vlasov-Maxwell systems, are computationally too expensive because they take into account all…

Analysis of PDEs · Mathematics 2012-04-23 Frédérique Charles , Bruno Després , Benoît Perthame , Remi Sentis

The control of plasma-wall interactions is crucial to fusion devices from both physical and mathematical perspectives. It is well known that a magnetic field satisfying the classical perfect conducting conditions at the wall, $$ \mathbf{E}…

Analysis of PDEs · Mathematics 2024-12-17 Hongjie Dong , Yan Guo , Timur Yastrzhembskiy

In this article, we study a collisionless kinetic model for plasmas in the neighborhood of a cylindrical metallic Langmuir probe. This model consists in a bi-species Vlasov-Poisson equation in a domain contained between two cylinders with…

Analysis of PDEs · Mathematics 2022-02-11 Mehdi Badsi , Ludovic Godard-Cadillac

We study existence and uniqueness of the solution to the Vlasov-Poisson system describing a plasma constituted by different species evolving in $\mathbb{R}^3$, whose particles interact via the Coulomb potential. The species can have both…

Mathematical Physics · Physics 2019-12-03 Silvia Caprino , Guido Cavallaro , Carlo Marchioro

We prove the global well-posedness for the 3-D micropolar fluid system in the critical Besov spaces by making a suitable transformation to the solutions and using the Fourier localization method, especially combined with a new $L^p$…

Analysis of PDEs · Mathematics 2011-12-20 Qionglei Chen , Changxing Miao