Related papers: A non-variational approach to nonlinear stability …
We study the existence of stationary solutions of the Vlasov-Poisson system with finite radius and finite mass in the stellar dynamics case. So far, the existence of such solutions is known only under the assumption of spherical symmetry.…
We complete previous investigations on the dynamical stability of barotropic stars and collisionless stellar systems. A barotropic star that minimizes the energy functional at fixed mass is a nonlinearly dynamically stable stationary…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…
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…
The kinetic motion of the stars of a galaxy is considered within the framework of a relativistic scalar theory of gravitation. This model, even though unphysical, may represent a good laboratory where to study in a rigorous, mathematical…
Spherical stellar systems such as King models, in which the distribution function is a decreasing function of energy and depends on no other invariant, are stable in the sense of collisionless dynamics. But Weinberg showed, by a clever…
A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through…
We prove a sufficient condition for nonlinear stability of relative equilibria in the planar $N$-vortex problem. This result builds on our previous work on the Hamiltonian formulation of its relative dynamics as a Lie--Poisson system. The…
We consider stability of non-rotating viscous gaseous stars modeled by the Navier-Stokes-Poisson system. Under general assumptions on the equations of states, we proved that the number of unstable modes for the linearized…
We propose a novel method applied to extrasolar planetary dynamics to describe the system stability. The observations in this field serve the measurements mainly of radial velocity, transit time, and/or celestial position. These scalar time…
In this paper we prove the nonlinear orbital stability of a large class of steady states solutions to the Hamiltonian Mean Field (HMF) system with a Poisson interaction potential. These steady states are obtained as minimizers of an energy…
We use the compactness result of A. Burchard and Y. Guo (cf. \cite{BuGu}) to analyze the reduced 'energy' functional arising naturally in the stability analysis of steady states of the Vlasov-Poisson system (cf. \cite{SaSo} and \cite{Ha}).…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…
Using a Liao-type exponent, we study the stability of a time-varying nonlinear switching system.
Using spatial domain techniques developed by the authors and Myunghyun Oh in the context of parabolic conservation laws, we establish under a natural set of spectral stability conditions nonlinear asymptotic stability with decay at Gaussian…
We obtain a natural extension of the Vlasov-Poisson system for stellar dynamics to spaces of constant Gaussian curvature $\kappa\ne 0$: the unit sphere $\mathbb S^2$, for $\kappa>0$, and the unit hyperbolic sphere $\mathbb H^2$, for…
This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general…
We consider an ensemble of mass collisionless particles, which interact mutually either by an attraction of Newton's law of gravitation or by an electrostatic repulsion of Coulomb's law, under a background downward gravity in a…
We study local well-posedness and orbital stability/instability of standing waves for a first order system associated with a nonlinear Klein-Gordon equation on a star graph. The proof of the well-posedness uses a classical fixed point…
The Nordstr\"om-Vlasov system is a relativistic Lorentz invariant generalization of the Vlasov-Poisson system in the gravitational case. The asymptotic behavior of solutions and the non-linear stability of steady states are investigated. It…