Related papers: Sharp asymptotics for the solutions of the three-d…
This paper investigates nonlinear Landau damping in the 3D Vlasov-Poisson (VP) system. We study the asymptotic stability of the Poisson equilibrium $\mu(v)=\frac{1}{\pi^2(1+|v|^2)^2}$ under small perturbations. Building on the foundational…
We consider a modified version of the Vlasov-Maxwell system in which the usual Maxwell fields are replaced by their retarded parts. We show that solutions of this modified system exist globally for a small number of particles and that they…
This paper continues the investigation of the formation of naked singularities in the collapse of collisionless matter initiated in [RV]. There the existence of certain classes of non-smooth solutions of the Einstein-Vlasov system was…
We present a microscopic derivation of the 3-dimensional relativistic Vlasov-Maxwell system as a combined mean field and point-particle limit of an $N$-particle system of rigid charges with $N$-dependent radius. The approximation holds for…
The aim of this article is to demonstrate how the vector field method of Klainerman can be adapted to the study of transport equations. After an illustration of the method for the free transport operator, we apply the vector field method to…
In this paper, we study the global well-posedness and decay rates of strong solutions to an incompressible Vlasov-MHD model arising in magnetized plasmas. This model is consist of the Vlasov equation and the incompressible…
The dynamics of collisionless plasmas can be modelled by the Vlasov-Maxwell system of equations. An Eulerian approach is needed to accurately describe processes that are governed by high energy tails in the distribution function, but is of…
We investigate the asymptotic stability of solutions to the characteristic initial value problem for the Einstein (massless) scalar field system with a positive cosmological constant. We prescribe spherically symmetric initial data on a…
This paper investigates the three-dimensional axisymmetric compressible Navier-Stokes equations under slip boundary conditions in a cylindrical domain excluding the axis. For initial density allowed to vanish, we establish the global…
This paper is devoted to the large time behavior of weak solutions to the three-dimensional Vlasov-Navier-Stokes system set on the half-space, with an external gravity force. This fluid-kinetic coupling arises in the modeling of…
This paper studies the nonlinear Landau damping on the torus $\mathbb{T}^d$ for the Vlasov-Poisson system with massless electrons (VPME). We consider solutions with analytic or Gevrey ($\gamma > 1/3$) initial data, close to a homogeneous…
In this paper, the Cauchy problem for the three-dimensional (3-D) isentropic compressible Navier-Stokes equations with degenerate viscosities is considered. By introducing some new variables and making use of the "quasi-symmetric…
This paper is devoted to the study of asymptotic behaviors of solutions to the one-dimensional defocusing semilinear wave equation. We prove that finite energy solution tends to zero in the pointwise sense, hence improving the averaged…
We show that weak solutions of the relativistic Vlasov-Maxwell system preserve the total energy provided that the electromagnetic field is locally of bounded variation and, for any $\lambda$> 0, the one-particle distribution function has a…
This paper studies the Cauchy problem for three-dimensional viscous, compressible, and heat conducting magnetohydrodynamic equations with vacuum as far field density. We prove the global existence and uniqueness of strong solutions provided…
We study the Cauchy problem for the reduced Maxwell-Bloch equations with initial data for the electric field in weighted Sobolev spaces, assuming that all atoms initially reside in their ground state. Using the d-bar steepest descent…
In this paper, we consider the three dimensional Vlasov equation with an inhomogeneous, varying direction, strong magnetic field. Whenever the magnetic field has constant intensity, the oscillations generated by the stiff term are periodic.…
Euler--Maxwell systems describe the dynamics of inviscid plasmas. In this work, we consider an incompressible two-dimensional version of such systems and prove the existence and uniqueness of global weak solutions, uniformly with respect to…
We study the asymptotic behavior of small data solutions to the screened Vlasov-Poisson equation on $\mathbb{R}^d\times\mathbb{R}^d$ near vacuum. We show that for dimensions $d\geq 2$, under mild assumptions on localization (in terms of…
Two fundamental models in plasma physics are given by the Vlasov-Maxwell-Boltzmann system and the compressible Euler-Maxwell system which both capture the complex dynamics of plasmas under the self-consistent electromagnetic interactions at…