Related papers: Stabilities for Euler-Poisson Equations in Some Sp…
We study static, spherically symmetric equilibrium configurations in extended theories of gravity (ETG) following the notation introduced by Capozziello et {\it al}. We calculate the differential equations for the stellar structure in such…
In this paper, we consider an isothermal Euler-Poisson system with self-gravitational force, modeling a compact star such as strange quark star. We prove that there exists a global entropy solution with spherically symmetry outside a ball,…
We consider the pressureless Euler-Poisson equations with quadratic confinement. For spatial dimension $d\ge 2,\,d\ne 4$, we give a necessary and sufficient condition for the existence of radial global smooth solutions, which is formulated…
We investigate the existence, uniqueness, and radial symmetry of normalized solutions to the Schr\"{o}dinger Poisson equation with non-autonomous nonlinearity $f(x,u)$: \begin{equation} -\triangle u+(|x|^{-1}*|u|^2)u=f(x,u)+\lambda u,…
In this paper we consider a nonlinear Petrovsky equation in a bounded domain with a delay term and a strong dissipation \begin{align*} u_{tt} + \Delta^{2} u -\mu_1g_1( \Delta( u_t(x,t))) -\mu_2g_2( \Delta (u_t(x,t-\tau))) =0. \end{align*}…
In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensional Euler equations. We use an adaptation of Kelvin's…
In this paper, we are concerned with the compressible Euler-Maxwell equations with a nonconstant background density (e.g. of ions) in three dimensional space. There exist stationary solutions when the background density is a small…
We present an analysis of the stability, energy and torque properties of a model Bursian diode in a one dimensional Eulerian framework using the cold Euler-Poisson fluid equations. In regions of parameter space where there are two sets of…
We study the asymptotic behavior and the asymptotic stability of the two-dimensional Euler equations and of the two-dimensional linearized Euler equations close to parallel flows. We focus on spectrally stable jet profiles $U(y)$ with…
Our aim is to establish the global existence of classical solutions to the nonlinear irrotational Euler--Nordstr\"om system, which incorporates a linear equation of state and a cosmological constant. In this setting, gravitation is…
The well-posedness for the supersonic solutions of the Euler-Poisson system for hydrodynamical model in semiconductor devices and plasmas is studied in this paper. We first reformulate the Euler-Poisson system in the supersonic region into…
The cosmological dynamics of a non-locally corrected gravity theory, involving a power of the inverse d'Alembertian, is investigated. Casting the dynamical equations into local form, the fixed points of the models are derived, as well as…
We investigate the global in time stability of regular solutions with large velocity vectors to the evolutionary Navier-Stokes equation in ${\bf R}^3$. The class of stable flows contains all two dimensional weak solutions. The only…
We consider the 2D Euler equation of incompressible fluids on a strip and prove the stability of the rectangular stationary state.
In this paper a nonlinear Euler-Poisson-Darboux system is considered. In a first part, we proved the genericity of the hypergeometric functions in the development of exact solutions for such a system in some special cases leading to Bessel…
The Euler-Maxwell system describes the evolution of a plasma when the collisions are important enough that each species is in a hydrodynamic equilibrium. In this paper we prove global existence of small solutions to this system set in the…
In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for the stability in probability of stochastic dynamical systems with symmetries and…
We investigate spherically symmetric equilibrium states of the Vlasov-Poisson system, relevant in galactic dynamics. We recast the equations into a regular three-dimensional system of autonomous first order ordinary differential equations…
In this paper we examine the linear stability of equilibrium solutions to incompressible Euler's equation in 2- and 3-dimensions. The space of perturbations is split into two classes - those that preserve the topology of vortex lines and…
The 2D Euler equations are a simple but rich set of non-linear PDEs that describe the evolution of an ideal inviscid fluid, for which one dimension is negligible. Solving numerically these equations can be extremely demanding. Several…