MULTIPLE STATIONARY SOLUTIONS OF EULER-POISSON EQUATIONS FOR NON-ISENTROPIC GASEOUS STARS

The motion of the self-gravitational gaseous stars can be described by the Euler-Poisson equations. The main purpose of this paper is concerned with the existence of stationary solutions of Euler-Poisson equations for some velocity fields and entropy functions that solve the conservation of mass and energy. Under different restriction to the strength of velocity field, we get the existence and multiplicity of the stationary solutions of Euler-Poisson system.

UNIQUENESS OF STATIONARY SOLUTIONS WITH VACUUM OF EULER-POISSON EQUATIONS

In this paper, the uniqueness of stationary solutions with vacuum of Euler-Poisson equations is considered. Through a nonlinear transformation which is a function of density and entropy, the corresponding problem can be reduced to a semilinear elliptic equation with a nonlinear source term consisting of a power function, for which the classical theory of the elliptic equations leads the authors to the uniqueness result under some assumptions on the entropy function S(x). As an example, the authors get the uniqueness of stationary solutions with vacuum of Euler-Poisson equations for S(x) =|x|θandθ∈{0}∪[2(N-2),+∞).

A NOTE ON THE EXISTENCE OF STATIONARY SOLUTIONS OF THE COMPRESSIBLE EULER-POISSON EQUATIONS WITH 6/5<γ<2

This paper is concerned with the system of Euler-Poisson equations as a model to describe the motion of the self-induced gravitational gaseous stars. When ~ 〈 7 〈 2, under the weak smoothness of entropy function, we find a sufficient condition to guarantee the existence of stationary solutions for some velocity fields and entropy function that solve the conservation of mass and energy.

SOLUTIONS OF EULER-POISSON EQUATIONS IN R^n

In this article, the authors study the structure of the solutions for the EuierPoisson equations in a bounded domain of Rn with the given angular velocity and n is an odd number. For a ball domain and a constant angular velocity, both existence and nonexistence theorem are obtained depending on the adiabatic gas constant 7. In addition, they obtain the monotonicity of the radius of the star with both angular velocity and center density. They also prove that the radius of a rotating spherically symmetric star, with given constant angular velocity and constant entropy, is uniformly bounded independent of the central density. This is different to the case of the non-rotating star.

A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters： the nonlinearity ratio ε, represented by the ratio of amplitude to depth, and the dispersion ratio μ, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O（μ^2）. As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

GLOBAL WEAK SOLUTIONS TO THE α-MODEL REGULARIZATION FOR 3D COMPRESSIBLE EULER-POISSON EQUATIONS

Global in time weak solutions to the α-model regularization for the three dimensional Euler-Poisson equations are considered in this paper. We prove the existence of global weak solutions to α-model regularization for the three dimension compressible EulerPoisson equations by using the Fadeo-Galerkin method and the compactness arguments on the condition that the adiabatic constant satisfies γ >4/3.

Nonlinear Schrödinger Approximation for the Electron Euler-Poisson Equation

The nonlinear Schr?dinger(NLS for short)equation plays an important role in describing slow modulations in time and space of an underlying spatially and temporarily oscillating wave packet.In this paper,the authors study the NLS approximation by providing rigorous error estimates in Sobolev spaces for the electron Euler-Poisson equation,an important model to describe Langmuir waves in a plasma.They derive an approximate wave packet-like solution to the evolution equations by the multiscale analysis,then they construct the modified energy functional based on the quadratic terms and use the rotating coordinate transform to obtain uniform estimates of the error between the true and approximate solutions.

Structure-Preserving Finite-Element Schemes for the Euler-Poisson Equations

We discuss structure-preserving numerical discretizations for repulsive and attractive Euler-Poisson equations that find applications in fluid-plasma and selfgravitation modeling.The scheme is fully discrete and structure preserving in the sense that it maintains a discrete energy law,as well as hyperbolic invariant domain properties,such as positivity of the density and a minimum principle of the specific entropy.A detailed discussion of algorithmic details is given,as well as proofs of the claimed properties.We present computational experiments corroborating our analytical findings and demonstrating the computational capabilities of the scheme.

Global Smooth Solutions to Relativistic Euler-Poisson Equations with Repulsive Force

In this paper, we are concerned with the global existence of smooth solutions for the one dimen- sional relativistic Euler-Poisson equations： Combining certain physical background, the relativistic Euler-Poisson model is derived mathematically. By using an invariant of Lax＇s method, we will give a sufficient condition for the existence of a global smooth solution to the one-dimensional Euler-Poisson equations with repulsive force.

An Interface-Capturing Method for Resolving Compressible Two-Fluid Flows with General Equation of State

In this study,a stable and robust interface-capturing method is developed to resolve inviscid,compressible two-fluid flows with general equation of state(EOS).The governing equations consist of mass conservation equation for each fluid,momentum and energy equations for mixture and an advection equation for volume fraction of one fluid component.Assumption of pressure equilibrium across an interface is used to close the model system.MUSCL-Hancock scheme is extended to construct input states for Riemann problems,whose solutions are calculated using generalized HLLC approximate Riemann solver.Adaptive mesh refinement(AMR)capability is built into hydrodynamic code.The resulting method has some advantages.First,it is very stable and robust,as the advection equation is handled properly.Second,general equation of state can model more materials than simple EOSs such as ideal and stiffened gas EOSs for example.In addition,AMR enables us to properly resolve flow features at disparate scales.Finally,this method is quite simple,time-efficient and easy to implement.

LARGE-TIME BEHAVIOR OF SOLUTIONS OF QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

A one-dimensional quantum hydrodynamic model （or quantum Euler-Poisson system） for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of the classical solution of the corresponding steady-state quantum hydrodynamic equations is proved. Furthermore, the global existence of classical solution, when the initial datum is a perturbation of t he steadystate solution, is obtained. This solution tends to the corresponding steady-state solution exponentially fast as the time tends to infinity.

STABILITY OF GASEOUS STARS IN THE NON-ISENTROPIC CASE

The motion of the self-gravitational gaseous stars can be described by the Euler-Poisson equations. The main purpose of this article is concerned with the nonlinear stability of gaseous stars in the non-isentropic case, when 34 γ2, S（x,t） is a smooth bounded function. First, we verify that the steady states are minimizers of the energy via concentration-compactness method; then using the variational approach we obtain the stability results of the non-isentropic flow.

Dynamic Equations for Debris Flow

1 Fundamental Equations of Two-fluid Model The complicated debris flow is simplified as two-fluid model of solid and liquid two-phase flow,of which the liquid phase is slurry with the fine particle and the solid phase is the coarse particle separated from slurry.The movement of each phase may be described by using a group of equations.The interaction of the two phases is cou-

Quasi-neutral limit of the full bipolar Euler-Poisson system

The quasi-neutral limit of the multi-dimensional non-isentropic bipolar Euler-Poisson system is considered in the present paper. It is shown that for well-prepared initial data the smooth solution of the non-isentropic bipolar Euler-Poisson system converges strongly to the compressible non-isentropic Euler equations as the Debye length goes to zero.

Dark matter with chiral symmetry admixed with hadronic matterin compact stars

Using the two-fluid Tolman-Oppenheimer-Volkoff equation,the properties of dark matter(DM)admixed neutron stars(DANSs)have been investigated.In contrast to previous studies,we find that an increase in the maximum mass and a decrease in the radius of 1.4 M_(⊙)NSs can occur simultaneously in DANSs.This stems from the ability of the equation of state(EOS)for DM to be very soft at low density but very stiff at high density.It is well known that the IU-FSU and XS models are unable to produce a neutron star(NS)with a maximum mass greater than 2.0 M_(⊙).However,by considering the IU-FSU and XS models for DANSs,there are interactions with DM that can produce a maximum mass greater than 2.0 M_(⊙)and a radius of 1.4 M_(⊙)NSs below 13.7 km.When considering a DANS,the difference between DM with chiral symmetry(DMC)and DM with meson exchange(DMM)becomes obvious when the central energy density of DM is greater than that of nuclear matter(NM).In this case,the DMC model with a DM mass of 1000 MeV can still produce a maximum mass greater than 2.0 M_(⊙)and a radius of a 1.4 M_(⊙)NS below 13.7 km.Additionally,although the maximum mass of the DANS using the DMM model is greater than 2.0 M_(⊙),the radius of a 1.4 M_(⊙)NS can surpass 13.7 km.In the two-fluid system,the maximum mass of a DANS can be larger than 3.0 M_(⊙).Consequently,the dimensionless tidal deformabilityΛCP of a DANS with 1.4 M_(⊙),which increases with increasing maximum mass,may be larger than 800 when the radius of the 1.4 M_(⊙)DANS is approximately 13.0 km.

A Godunov-Type Solver for the Numerical Approximation of Gravitational Flows

We present a new numerical method to approximate the solutions of an Euler-Poisson model,which is inherent to astrophysical flows where gravity plays an important role.We propose a discretization of gravity which ensures adequate coupling of the Poisson and Euler equations,paying particular attention to the gravity source term involved in the latter equations.In order to approximate this source term,its discretization is introduced into the approximate Riemann solver used for the Euler equations.A relaxation scheme is involved and its robustness is established.The method has been implemented in the software HERACLES[29]and several numerical experiments involving gravitational flows for astrophysics highlight the scheme.

Boundary Plasma Turbulence Simulations for Tokamaks

The boundary plasma turbulence code BOUT models tokamak boundaryplasma turbulence in a realistic divertor geometry usingmodified Braginskii equations for plasma vorticity,density(ni),electron and ion temperature(Te,Ti)and parallelmomenta.The BOUT code solves for the plasma fluid equations in a three dimensional(3D)toroidal segment(or a toroidal wedge),including the region somewhat inside the separatrix and extending into the scrape-off layer;the private flux region is also included.In this paper,a description is given of the sophisticated physical models,innovative numerical algorithms,and modern software design used to simulate edgeplasmas in magnetic fusion energy devices.The BOUT code’s unique capabilities and functionality are exemplified via simulations of the impact of plasma density on tokamak edge turbulence and blob dynamics.