Related papers: Existence for Stable Rotating Star-Planet Systems
The paper considers Euler-Poisson equations which govern the steady state of a self gravitating, rotating, axi-symmetric stars under the additional assumption that it is composed of incompressible stratified fluid. The original system of…
Goldreich-Weber solutions constitute a finite-parameter of expanding and collapsing solutions to the mass-critical Euler-Poisson system. Two subclasses of this family correspond to compactly supported density profiles suitably modulated by…
We present solutions to the Einstein-Klein Gordon system representing boson stars in the slow rotation approximation. By considering slow rotation we are able to reduce the number of equations yielding a system of ordinary differential…
For the one-dimensional mass-critical/supercritical pseudo-relativistic nonlinear Schrodinger equation, a stationary solution can be constructed as an energy minimizer under an additional kinetic energy constraint and the set of energy…
This paper deals with the existence of travelling wave solutions for a general one-dimensional nonlinear Schr\"odinger equation. We construct these solutions by minimizing the energy under the constraint of fixed momentum. We also prove…
Observations indicate that members of close stellar binaries often have mass ratios close to unity, while longer-period systems exhibit a more uniform mass-ratio distribution. This paper provides a theoretical explanation for this finding…
In this paper we investigate the existence of solutions in $H^1(R^N) \times H^1(R^N)$ for nonlinear Schr\"odinger systems of the form \[ \left\{ \begin{aligned} -\Delta u_1 &= \lambda_1 u_1 + \mu_1 |u_1|^{p_1 -2}u_1 + r_1\beta…
We prove the existence and nonlinear stability of steady states of the Vlasov-Poisson system in the stellar dynamics case. The steady states are obtained as minimizers of an energy-Casimir functional from which fact their dynamical…
This paper explores the stability of an Earth-like planet orbiting a solar mass star in the presence of an outer-lying intermediate mass companion. The overall goal is to estimate the fraction of binary systems that allow Earth-like planets…
We consider compact boson stars that arise for a V-shaped scalar field potential. They represent a one parameter family of solutions of the scaled Einstein-signum-Gordon equations. We analyze the physical properties of these solutions and…
We prove the existence and nonlinear stability of Camm type steady states of the Vlasov-Poisson system in the gravitational case. The paper demonstrates the effectiveness of an approach to the existence and stability problem for steady…
This paper investigates the stability of traveling wave solutions to the free boundary Euler equations with a submerged point vortex. We prove that sufficiently small-amplitude waves with small enough vortex strength are conditionally…
We consider the problem of existence of constrained minimizers for the focusing mass-subcritical Half-Wave equation with a defocusing mass-subcritical perturbation. We show the existence of a critical mass such that minimizers do exist for…
We prove the following theorem: axisymmetric, stationary solutions of the Einstein field equations formed from classical gravitational collapse of matter obeying the null energy condition, that are everywhere smooth and ultracompact (i.e.,…
In this article, we study small perturbations of the family of Friedmann-Lema\^itre-Robertson-Walker cosmological background solutions to the Euler-Einstein system with a positive cosmological constant in 1 + 3 dimensions. The background…
In 2001 Wolansky \cite{Wol} introduced a particle number-Casimir functional for the Einstein-Vlasov system. Two open questions are associated with this functional. First, a meaningful variational problem should be formulated and the…
Multi-planet systems detected until now are in most cases characterized by hot-Jupiters close to their central star as well as high eccentricities. As a consequence, from a dynamical point of view, compact multi-planetary systems form a…
We study the existence and structure of static and slowly rotating neutron stars (NSs) in a particular truncation of scalar torsion theory with a scalar field $ \phi $ non-minimally coupled to the torsion scalar, and a potential of the form…
The majority of star formation results in binaries or higher multiple systems, and planets in such systems are constrained to a limited range of orbital parameters in order to remain stable against perturbations from stellar companions.…
The classical model of a star is the Lane-Emden star with dynamics governed by the Euler-Poisson equations. We consider the case of a liquid star with a "stiffened gas" equation of state $p=\rho^\gamma-1$. We derive the full 3D linearised…