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

We establish a hierarchy of Euclidean stars according to their degree of complexity, as measured by the complexity factor and the complexity of the pattern of evolution. We consider both, nondissipative and dissipative systems. Solutions…

Two-dimensional gas dynamics equations in mass Lagrangian coordinates are studied in this paper. The equations describing these flows are reduced to two Euler-Lagrange equations. Using group classification and Noether's theorem,…

A gas composed of a large number of atoms evolving according to Newtonian dynamics is often described by continuum hydrodynamics. Proving this rigorously is an outstanding open problem, and precise numerical demonstrations of the…

In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…

In this note we survey some recent results for the Euler equations in compressible and incompressible fluid dynamics. The main point of all these theorems is the surprising fact that a suitable variant of Gromov's $h$-principle holds in…

The stability of equilibrium configurations of galaxies or stars are time honored problems in astrophysics. We present mathematical results on these problems which have in recent years been obtained by Yan Guo and the author in the context…

The problem of galaxy formation and its dependence on thermodynamic properties is addressed by using Eulerian hydrodynamic numerical simulations of large scale structure formation. Global galaxy properties are explored in simulations…

Most numerical models of binary stars - in particular neutron stars in compact binaries - assume the companions to be either corotational or irrotational. Either one of these assumptions leads to a significant simplification in the…

We describe the theory and implementation of a three-dimensional fluid dynamics code which we have developed for calculating the surface geometry and circulation currents in the secondaries of interacting binary systems. The main method is…

We review a series of recent results on global dynamic properties of radially symmetric self-gravitating compressible Euler flows, which naturally arise in the mathematical description of stars. We focus on the role of scaling invariances…

This paper contains a rigorous mathematical example of direct derivation of the system of Euler hydrodynamic equations from Hamiltonian equations for N point particle system as N tends to infinity. Direct means that the following standard…

This review is a short introduction to numerical hydrodynamics in a cosmological context, intended for the non specialist. The main processes relevant to galaxy formation are first presented. The fluid equations are then introduced, and…

Compressible Euler-Poisson equations are the standard self-gravitating models for stellar dynamics in classical astrophysics. In this article, we construct periodic solutions to the isothermal ($\gamma=1$) Euler-Poisson equations in $R^{2}$…

This paper presents a systematic study of the properties of non-rotating stellar models governed by the Euler-Poisson system under general equations of state, including the case of polytropic gaseous stars. We revisit and extend existence…

The planetary effective surface temperature alone is insufficient to characterize exoplanet atmospheres and their stability or evolution. Considering the star-planet system as a whole is necessary, and a critical component of the system is…

The hydrodynamic equations for a model of a confined quasi-two-dimensional gas of smooth inelastic hard spheres are derived from the Boltzmann equation for the model, using a generalization of the Chapman-Enskog method. The heat and…

The physics of stars, their workings and their evolution, is a goldmine of problems in statistical mechanics and thermodynamics. We discuss many examples that illustrate the possibility of deepening student's knowledge of statistical…

Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…

We present an efficient technique to study the 1D evolution of instability-generated structure in winds of hot stars out to very large distances (more than 1000 stellar radii). This technique makes use of our previous finding that external…

This article is the continued version of the analytical blowup solutions for 2-dimensional Euler-Poisson equations in "M.W. Yuen, Analytical Blowup Solutions to the 2-dimensional Isothermal Euler-Poisson Equations of Gaseous Stars, J. Math.…