Related papers: Stability Properties of the Riemann Ellipsoids

This is the second paper in a series studying the nonlinear stability of rarefaction waves in multi-dimensional gas dynamics. We construct initial data near singularities in the rarefaction wave region and, combined with the a priori energy…

This paper is devoted to the study of Lyapunov type inequalities for periodic conservative systems. The main results are derived from a previous analysis which relates the best Lyapunov constants to some especial (constrained or…

In a Riemannian manifold with a smooth positive function that weights the associated Hausdorff measures we study stable sets, i.e., second order minima of the weighted perimeter under variations preserving the weighted volume. By assuming…

This paper investigates Nekhoroshev-type stability for solutions of ultra-differentiable regularity in Schr\"odinger equations with non-local nonlinear terms, employing the method of rational normal forms. We establish the first rigorous…

This paper studies the uniformly asymptotic stability of nonautonomous systems on Riemannian manifolds. We establish corresponding Lyapunov-type theorems (Theorems 2.1 and 2.2), extending classical Euclidean results (e.g., [9, Theorems 4.9…

We establish Liouville type theorems for elliptic systems with various classes of non-linearities on $\mathbb{R}^N$. We show among other things, that a system has no semi-stable solution in any dimension, whenever the infimum of the…

Let L be a Lagrangian submanifold of a pseudo- or para-K\"ahler manifold which is H-minimal, i.e. a critical point of the volume functional restricted to Hamiltonian variations. We derive the second variation of the volume of L with respect…

The stability features of steady states of the spherically symmetric Einstein-Vlasov system are investigated numerically. We find support for the conjecture by Zeldovich and Novikov that the binding energy maximum along a steady state…

We investigate the long time stability in Nekhoroshev's sense for the Sun-Jupiter-Saturn problem in the framework of the problem of three bodies. Using computer algebra in order to perform huge perturbation expansions we show that the…

In this short paper we prove a global logarithmic stability of the Cauchy problem for H 2-solutions of an anisotropic elliptic equation in a Lip-schitz domain. The result we obtained is based on tools borrowed from the existing technics to…

We consider steady state solutions of the massive, asymptotically flat, spherically symmetric Einstein-Vlasov system, i.e., relativistic models of galaxies or globular clusters, and steady state solutions of the Einstein-Euler system, i.e.,…

The possible observations of Trojan-like extrasolar planets stimulate the deeper understanding of the stability behaviour of the co-orbital resonant motion. By using Hill's equations and the energy-rate method an analysis of the stability…

We study the linear stability problem to gravitational and electromagnetic perturbations of the extremal, $ |\mathcal{Q}|=M, $ Reissner-Nordstr\"om spacetime, as a solution to the Einstein-Maxwell equations. Our work uses and extends the…

Near-rectilinear halo orbits (NRHOs) around Earth-Moon L2 in the Circular Restricted 3-Body Problem (CR3BP) exhibit a complex dynamical landscape, featuring a band of normally elliptic orbits embedded within regions of strong instability.…

I report on recent work concerning the existence and stability of self-gravitating spheres with anisotropic pressure. After presenting new exact solutions, Chandrasekhar's variational formalism for radial perturbations is generalized to…

We study the stability properties of the Kidder-Scheel-Teukolsky (KST) many-parameter formulation of Einstein's equations for weak gravitational waves on flat space-time from a continuum and numerical point of view. At the continuum,…

The paper introduces and studies the notions of Lipschitzian and H\"olderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial…

Double averaged planar restricted elliptic three-body problem has a two-parametric family of stable equilibria. We show that these equilibria are stable in the linear approximation as equilibria of the double averaged spatial restricted…

The article treats the classical problem of stability of steady rotation of a rigid homogeneous ellipsoid on a rigid smooth plane which rotates about its vertical axis. The condition for the steady rotation is derived from the Euler-Poisson…

We characterize several stability properties, such as inverse or composition closedness, for ultraholomorphic function classes of Roumieu type defined in terms of a weight matrix. In this way we transfer and extend known results from J.…