相关论文: Two-dimensional Finite Larmor Radius approximation…
Consider the Vlasov-Poisson-Landau system with Coulomb potential in the weakly collisional regime on a $3$-torus, i.e. $$\begin{aligned} \partial_t F(t,x,v) + v_i \partial_{x_i} F(t,x,v) + E_i(t,x) \partial_{v_i} F(t,x,v) = \nu…
We prove a sharp decoupling for a certain two dimensional surface in R^9. As an application, we obtain the full range of expected estimates for the cubic Parsell-Vinogradov system in two dimensions.
In this paper, we are concerned with the global well-posedness and time-asymptotic decay of the Vlasov-Fokker-Planck equation with local alignment forces. The equation can be formally derived from an agent-based model for self-organized…
A new model, inspired by the structure of galactic disks, for three-dimensional Bernstein-Greene-Kruskal (BGK) modes in a plasma with a uniform finite background magnetic field is presented. These modes are exact nonlinear solutions of the…
We consider the $3$-dimensional relativistic Vlasov-Maxwell system with data without compact support in momentum space. We prove two continuation criteria for solutions to this system. First, we show that a regular solution can be continued…
We extend our previous work on a semi-Lagrangian adaptive rank (SLAR) integrator, in the finite difference framework for nonlinear Vlasov-Poisson systems, to the general high-order tensor setting. The proposed scheme retains the high-order…
In Newtonian gravity, a self-gravitating collisionless gas around a massive object such as a star or a planet is modeled via the Vlasov--Poisson system with an external Kepler potential. The presence of this attractive potential allows for…
We consider two-dimensional Coulomb systems confined in a disk with ideal dielectric boundaries. In particular we study the two-component plasma in detail. When the coulombic coupling constant $\Gamma=2$ the model is exactly solvable. We…
In this paper we establish best approximation property of fully discrete Galerkin solutions of second order parabolic problems on convex polygonal and polyhedral domains in the $L^\infty(I;W^{1,\infty}(\Om))$ norm. The discretization method…
A method to derive stationary solutions of the relativistic Vlasov-Maxwell system is explored. In the non-relativistic case, a method using the Hermite polynomial series to describe the deviation from the Maxwell-Boltzmann distribution is…
Spectral approximation based on Hermite-Fourier expansion of the Vlasov-Poisson model for a collisionless plasma in the electro-static limit is provided, by including high-order artificial collision operators of Lenard-Bernstein type. These…
A new procedure for the global construction of the Casimir invariants and Darboux canonical form for finite-dimensional Poisson systems is developed. This approach is based on the concept of matrix congruence and can be applied without the…
The foundations of gyrokinetic theory are reviewed with an emphasis on the applications of Lagrangian and Hamiltonian methods used in the derivation of nonlinear gyrokinetic Vlasov-Maxwell equations. These reduced dynamical equations…
We consider the complete set of planar two-loop five-point Feynman integrals with two off-shell external legs. These integrals are relevant, for instance, for the calculation of the second-order QCD corrections to the production of two…
A new fully discrete linearized $H^1$-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical…
We study the dynamics of two-dimensional interacting fermions submitted to a homogeneous transverse magnetic field. We consider a large magnetic field regime, with the gap between Landau levels set to the same order as that of potential…
In this paper, we construct unique, local-in-time strong solutions to the Vlasov-Poisson (VP) and Vlasov-Poisson-Fokker-Planck (VPFP) systems subjected to external, spatially regular, white-in-time electromagnetic fields in $\mathbb T^d…
This work presents the continuation of the recent article "The Lorenz system: hidden boundary of practical stability and the Lyapunov dimension", published in the Nonlinear Dynamics journal. In this work, in comparison with the results for…
Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are approximated by equations of the discrete nonlinear Schrodinger type. We show how to justify this approximation by two methods, which have been very popular in the…
We derive the equations of motion for a planar rigid body of circular shape moving in a 2D perfect fluid with point vortices using symplectic reduction by stages. After formulating the theory as a mechanical system on a configuration space…