Related papers: Stability of disk-like galaxies--Part I: Stability…
In this paper, we are concerned with the structural stability of some steady subsonic solutions for Euler-Poisson system. A steady subsonic solution with subsonic background charge is proven to be structurally stable with respect to small…
We prove the stability of de Sitter space-time as a solution to the Einstein-Vlasov system with massless particles. The semi-global stability of Minkowski space-time is also addressed. The proof relies on conformal techniques, namely…
We prove the existence of orbitally stable standing waves with prescribed $L^2$-norm for the following Schr\"odinger-Poisson type equation \label{intro} %{%{ll} i\psi_{t}+ \Delta \psi - (|x|^{-1}*|\psi|^{2}) \psi+|\psi|^{p-2}\psi=0…
Linear stability analysis of the axisymmetric interface of velocity and density discontinuity in rotating gaseous disk has been performed numerically and analytically. Physical mechanisms leading to development of centrifugal and…
The majority of disk galaxies manifest spirals and/or bars that are believed to result from dynamical instabilities. However, some galaxies have featureless disks, which are therefore inferred to be dynamically stable. Yet despite many…
We analyze the Drinfeld-Sokolob-Wilson system, which features a dispersive, KdV type evolution with a dispersionless conservation law. We establish well-posedness with low regularity initial data $L^2({\mathbb T})\times L^2({\mathbb T})$…
In high-temperature plasma physics, a strong magnetic field is usually used to confine charged particles. Therefore, for studying the classical mathematical models of the physical problems it needs to consider the effect of external…
In this paper, we prove the existence of two-dimensional solutions to the steady Euler-Poisson system with continuous transonic transitions across sonic interfaces of codimension 1. First, we establish the well-posedness of a boundary value…
Existence of spherically symmetric solutions to the Einstein-Vlasov system is well-known. However, it is an open problem whether or not static solutions arise as minimizers of a variational problem. Apart from being of interest in its own…
We consider Friedmann-like universes with torsion and take a step towards studying their stability. In so doing, we apply dynamical-system techniques to an autonomous system of differential equations, which monitors the evolution of these…
We study the stability under linear perturbations of a class of static solutions of Einstein-Gauss-Bonnet gravity in $D=n+2$ dimensions with spatial slices of the form $\Sigma_{\k}^n \times {\mathbb R}^+$, $\Sigma_{\k}^n$ an $n-$manifold of…
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…
This paper is a first step toward understanding the effect of toroidal geometry on the rigorous stability theory of plasmas. We consider a collisionless plasma inside a torus, modeled by the relativistic Vlasov-Maxwell system. The surface…
We consider the Einstein flow on a product manifold with one factor being a compact quotient of 3-dimensional hyperbolic space without boundary and the other factor being a flat torus of fixed arbitrary dimension. We consider initial data…
We present a computational study for a family of discontinuous Galerkin methods for the one dimensional Vlasov-Poisson system that has been recently introduced. We introduce a slight modification of the methods to allow for feasible…
We are interested in the stability analysis of two-dimensional incompressible inviscid fluids. Specifically, we revisit a recent result on the stability of Yudovich's solutions to the incompressible Euler equations in $L^\infty([0,T];H^1)$…
We provide a short proof of the $L^2$-orbital stability of a class of explicit steady Euler flows in a disk by establishing a quantitative estimate. The main idea is to exploit the conserved quantities of the Euler equation, including the…
We prove propagation of $\frac{1}{s}$-Gevrey regularity $(s\in(0,1))$ for the Vlasov-Poisson system on $\mathbb{T}^d$ using a Fourier space method in analogy to the results proved for the 2D Euler system in \cite{KV} and \cite{LO}. More…
The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. In the 3D case Guo first constructed a global smooth irrotational solution…
We consider the Schr\"odinger-Poisson system in the attractive (plasma physics) Coulomb case. Given a steady state from a certain class we prove its nonlinear stability, using an appropriately defined energy-Casimir functional as Lyapunov…