相关论文: Flat steady states in stellar dynamics - existence…
The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell (VM) system. These equations are considered in one space dimension and two momentum dimensions without the assumption…
This paper investigates the stability and large-time behavior of solutions to the rotating Boussinesq system under the influence of a general gravitational potential $\Psi$, which is widely used to model the dynamics of stratified…
We consider the steady-state Boussinesq system in the whole three-dimensional space, with the action of external forces and the gravitational acceleration. First, for $3<p\leq +\infty$ we prove the existence of weak $L^p$-solutions.…
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 general relativity static gaseous atmospheres may be in hydrostatic balance in the absence of a supporting stellar surface, provided that the luminosity is close to the Eddington value. We construct analytic models of optically thin,…
We consider the one-dimensional Vlasov equation with an attractive cosine potential, and its non homogeneous stationary states that are decreasing functions of the energy. We show that in the Sobolev space $W^{1,p}$ ($p>2$) neighborhood of…
Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density $\rho$ which either falls off at infinity or has compact support. The solutions have finite mass, finite…
We prove that the steady state of a class of multidimensional reaction-diffusion systems is asymptotically stable at the intersection of unweighted space and exponentially weighted Sobolev spaces, and pay particular attention to a special…
In this paper, we establish uniqueness of the solution of the Vlasov-Poisson system with spatial density belonging to a certain class of Orlicz spaces. This extends the uniqueness result of Loeper (which holds for uniformly bounded density)…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
We investigate the dynamical stability of a fully-coupled system of $N$ inertial rotators, the so-called Hamiltonian Mean Field model. In the limit $N \to \infty$, and after proper scaling of the interactions, the $\mu$-space dynamics is…
Relaxation processes in collisionless dynamics lead to peculiar behavior in systems with long-range interactions such as self-gravitating systems, non-neutral plasmas and wave-particle systems. These systems, adequately described by the…
We study the linearized Vlasov-Poisson system around suitably stable homogeneous equilibria on $\mathbb{R}^d\times \mathbb{R}^d$ (for any $d \geq 1$) and establish dispersive $L^\infty$ decay estimates in the physical space.
The Cauchy problem is revisited for the so-called relativistic Vlasov-Poisson system in the attractive case. Global existence and uniqueness of spherical classical solutions is proved under weaker assumptions than previously used. A new…
We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe…
We consider the Schr\"odinger--Poisson--Newton equations for crystals with a cubic lattice and one ion per cell. We linearize this dynamics at the ground state and introduce a novel class of the ion charge densities which provide the…
Dynamical system techniques are extremely useful to study cosmology. It turns out that in most of the cases, we deal with finite isolated fixed points corresponding to a given cosmological epoch. However, it is equally important to analyse…
We study the stabilities and classical solutions of Euler-Poisson equations of describing the evolution of the gaseous star in astrophysics. In fact, we extend the study the stabilities of Euler-Poisson equations with or without frictional…
We prove the convergence of a spectral discretization of the Vlasov-Poisson system. The velocity term of the Vlasov equation is discretized using either Hermite functions on the infinite domain or Legendre polynomials on a bounded domain.…
We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum methods.…