相关论文: Note on the descriptions of the Euler-Poisson equa…

In this second article of a series we propose to base criteria of stability on the hamiltonian functional that is provided by the variational principle, to replace the reliance that has often been placed on {\it ad hoc} definitions of the…

We describe a numerical method for calculating the (3+1) dimensional general relativistic hydrodynamics of a coalescing neutron-star binary system. The relativistic field equations are solved at each time slice with a spatial 3-metric…

This paper gives a condensed review of the history of solutions to the Euler-Poisson equations modeling equilibrium states of rotating stars and galaxies, leading to a recent result of Walter Strauss and the author. This result constructs a…

The Kepler problem is considered in a space with the Friedmann--Lemaitre--Robertson--Walker metrics of the expanding universe. The covariant differential of the Friedmann coordinates (X=a(t)x) is considered as a possible mechanism of the…

Stars and their exoplanets evolve together. Depending on the physical characteristics of these systems, such as age, orbital distance and activity of the host stars, certain types of star-exoplanet interactions can dominate during given…

Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscosity and heat transfer is taken into account. Exact solutions…

Hydrodynamic equations for a one-component plasma are derived as a generalization of the Euler equations to include the effects of the long-range Coulomb interaction. By using a variational principle, these equations self-consistently unify…

The fate of small particles in turbulent flows depends strongly on the surrounding fluid's velocity gradient properties such as rotation and strain-rates. For non-inertial (fluid) particles, the Restricted Euler model provides a simple,…

Modeling the outflow of planetary atmospheres is important for understanding the evolution of exoplanet systems and for interpreting their observations. Modern theoretical models of exoplanet atmospheres become increasingly detailed and…

Stars are essentially gravitationally stabilised thermonuclear reactors in hydrostatic equilibrium. The fundamental differential equation for all Newtonian gaseous stars in equilibrium is \begin{align}…

The evolution of exoplanetary systems with a close-in planet is ruled by the tides mutually raised on the two bodies and by the magnetic braking of the host star. This paper deals with consequences of this evolution and some features that…

The dynamics of cosmological gravitating system is governed by the Euler and the Poisson equations. Tiny fluctuations near the big bang singularity are amplified by gravitational instability into the observed structure today. Given the…

The four equations of stellar structure are reformulated as two alternate pairs of variational principles. Different thermodynamic representations lead to the same hydromechanical equations, but the thermal equations require, not the…

In this article, we address both recent advances and open questions in some mathematical and computational issues in geophysical fluid dynamics (GFD) and climate dynamics. The main focus is on 1) the primitive equations (PEs) models and…

In this introductory chapter of the Special Issue entitled `The Structure and Evolution of Stars', we highlight the recent major progress made in our understanding in the physics that governs stellar interiors. In so doing, we combine…

This paper studies the two-dimensional Euler-Poisson equations associated with either attractive or repulsive forces. We mainly study the Riccati system that governs the flow's gradient. Under a suitable condition, it is shown that the…

Generalized hydrodynamics (GHD) was proposed recently as a formulation of hydrodynamics for integrable systems, taking into account infinitely-many conservation laws. In this note we further develop the theory in various directions. By…

In this paper, we study the phase space of cosmological models in the context of Einstein-Gauss-Bonnet theory. More specifically, we consider a generalized dynamical system that encapsulates the main features of the theory and for the cases…

The Euler-Poisson(EP) system describes the dynamic behavior of many important physical flows. In this work, a Riccati system that governs the flow's gradient is studied. The evolution of divergence is governed by the Riccati type equation…

The status of the hydrodynamical modelling of nonlinear multi-mode stellar pulsations is discussed. The hydrodynamical modelling of steady double-mode (DM) pulsations has been a long-standing quest that is finally being concluded. Recent…