共查询到20条相似文献,搜索用时 15 毫秒
1.
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. 相似文献
2.
In this paper, we consider the Euler-Poisson equations governing the evolution of the gaseous stars with the Poisson equation describing the energy potential for the self-gravitating force. By assuming that the initial density is of compact support in , we first give a family of blowup solutions for non-isentropic polytropic gas when γ=(2N−2)/N which generalizes the known result for the isentropic case. Then we extend the previous result on non-blowup phenomena to the case when (2N−2)/N?γ<2 in N-dimensional space. Here γ is the adiabatic gas constant. 相似文献
3.
** Email: guo_zhenhua{at}iapcm.ac.cn*** Email: jiang{at}iapcm.ac.cn We investigate the self-similar solutions to the isothermalcompressible NavierStokes equations. The aim of thispaper is to show that there exist neither forward nor backwardself-similar solutions with finite total energy. This generalizesthe results for the incompressible case in Neas, J., Rika, M.& verák, V. (1996, On Leray's self-similar solutionsof the Navier-Stokes equations. Acta. Math., 176, 283294),and is consistent with the (unproved) existence of regular solutionsglobally in time for the compressible NavierStokes equations. 相似文献
4.
本文在R^(N)(N=2,3)中研究描述流向外部真空的可压缩流体的欧拉与欧拉-泊松方程组径向对称解的爆破.在分离流体与真空的连续自由边界条件下考虑其自由边值问题.对于径向对称的欧拉方程组,证明若初始流平均向外流动,则其光滑解将在有限时刻爆破.对于带有斥力与弛豫项的单极与双极径向对称欧拉-泊松方程组,证明若某个与初始动量有关的加权泛函适当大,则其光滑解将在有限时刻爆破。 相似文献
5.
In this paper, the Cauchy problem of the isothermal hydrodynamic model for semiconductor devices is investigated. The existence of global weak entropy solutions with large initial data is obtained by using a modified fractional step Lax-Friedrichs scheme and the theory of compensated compactness. As a byproduct, the existence of entropy solutions to the Cauchy problem of the isentropic hydrodynamic model for a semiconductor with infinite mass is also proved. 相似文献
6.
Shaohua Chen 《Journal of Mathematical Analysis and Applications》2004,293(1):227-236
The author discusses the initial-boundary value problem (ui)t=Δui+fi(u1,…,um) with and ui(x,0)=φi(x), i=1,…,m, in a bounded domain Ω⊂Rn. Under suitable assumptions on fi, he proves that, if φi?(1+ε0)ψi in , for some small ε0>0, then the solutions blow up in a finite time, where ψi is a positive solution of Δψi+fi(ψ1,…,ψm)?0, with ψi|∂Di=0 for i=1,…,m. If m=1, the initial value can be negative in a subset of Ω. 相似文献
7.
Huimin Yu 《Journal of Mathematical Analysis and Applications》2010,363(1):302-309
In this paper, the large time behavior of spherically symmetric weak solutions to the multi-dimensional isothermal Euler-Poisson system in an annulus is considered. When space dimension N=2, it is shown that the weak solutions converge to the unique stationary solution exponentially in time. No smallness and regularity conditions are assumed. 相似文献
8.
Yeping Li 《Journal of Mathematical Analysis and Applications》2008,342(2):1107-1125
In this paper, we investigate a multidimensional nonisentropic hydrodynamic (Euler-Poisson) model for semiconductors. We study the convergence of the nonisentropic Euler-Poisson equation to the incompressible nonisentropic Euler type equation via the quasi-neutral limit. The local existence of smooth solutions to the limit equations is proved by an iterative scheme. The method of asymptotic expansion and energy methods are used to rigorously justify the convergence of the limit. 相似文献
9.
The authors discuss the quasilinear parabolic equation ut=∇⋅(g(u)∇u)+h(u,∇u)+f(u) with u|∂Ω=0, u(x,0)=?(x). If f, g and h are polynomials with proper degrees and proper coefficients, they show that the blowup property only depends on the first eigenvalue of −Δ in Ω with Dirichlet boundary condition. For a special case, they obtain a sharp result. 相似文献
10.
In this paper, we study the quasi-neutral limit of compressible Euler-Poisson equations in plasma physics in the torus Td. For well prepared initial data the convergence of solutions of compressible Euler-Poisson equations to the solutions of incompressible Euler equations is justified rigorously by an elaborate energy methods based on studies on an λ-weighted Lyapunov-type functional. One main ingredient of establishing uniformly a priori estimates with respect to λ is to use the curl-div decomposition of the gradient. 相似文献
11.
In this note, we rigorously justify a singular approximation of the incompressible Navier-Stokes equations. Our approximation combines two classical approximations of the incompressible Euler equations: a standard relaxation approximation, but with a diffusive scaling, and the Euler-Poisson equations in the quasineutral regime.
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13.
This paper concerns the global existence and the large time behavior of strong and classical solutions to the two-dimensional (2D) Stokes approximation equations for the compressible flows. We consider the unique global strong solution or classical solution to the 2D Stokes approximation equations for the compressible flows together with the space-periodicity boundary condition or the no-stick boundary condition or Cauchy problem for arbitrarily large initial data. First, we prove that the density is bounded from above independent of time in all these cases. Secondly, we show that for the space-periodicity boundary condition or the no-stick boundary condition, if the initial density contains vacuum at least at one point, then the global strong (or classical) solution must blow up as time goes to infinity. 相似文献
14.
Filiz Ta?can 《Applied mathematics and computation》2009,215(8):3134-3139
In this paper, we establish exact solutions for (2 + 1)-dimensional nonlinear evolution equations. The sine-cosine method is used to construct exact periodic and soliton solutions of (2 + 1)-dimensional nonlinear evolution equations. Many new families of exact traveling wave solutions of the (2 + 1)-dimensional Boussinesq, breaking soliton and BKP equations are successfully obtained. These solutions may be important of significance for the explanation of some practical physical problems. It is shown that the sine-cosine method provides a powerful mathematical tool for solving a great many nonlinear partial differential equations in mathematical physics. 相似文献
15.
We integrate the equations of gas dynamics in finite form for the solutions in which the thermodynamic parameters depend only on one spatial variable. The corresponding motion of gas represents the nonlinear superposition of the one-dimensional gas motion corresponding to the invariant system and the two-dimensional motion determined by noninvariant functions. These motions are called 2.5-dimensional. We reduce the invariant system to a first-order implicit ordinary differential equation. We study various solutions of the latter. We construct some continuous and discontinuous solutions to the equations of gas dynamics and give their physical interpretation. 相似文献
16.
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. 相似文献
17.
The motion of the self‐gravitational gaseous stars can be described by the Euler–Poisson equations. For some velocity fields and entropy functions that solve the conservation of mass and energy, we consider the existence of stationary solutions of Euler–Poisson equations. Under various restriction to the strength of velocity field, different assumptions on the isentropic function and adiabatic exponent, we get the existence, multiplicity and uniqueness of the stationary solutions to the Euler–Poisson system, respectively. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
18.
Convergence of Compressible Euler-Maxwell Equations to Compressible Euler-Poisson Equations 总被引:2,自引:0,他引:2
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In this paper,the convergence of time-dependent Euler-Maxwell equations to compressible Euler-Poisson equations in a torus via the non-relativistic limit is studied. The local existence of smooth solutions to both systems is proved by using energy esti- mates for first order symmetrizable hyperbolic systems.For well prepared initial data the convergence of solutions is rigorously justified by an analysis of asymptotic expansions up to any order.The authors perform also an initial layer analysis for general initial data and prove the convergence of asymptotic expansions up to first order. 相似文献
19.
This paper concerns the large time behavior of strong and classical solutions to the two-dimensional Stokes approximation equations for the compressible flows. We consider the unique global strong solution or classical solution to the two-dimensional Stokes approximation equations for the compressible flows with large external potential force, together with a Navier-slip boundary condition, for arbitrarily large initial data. Under the conditions that the corresponding steady state exists uniquely with the steady state density away from vacuum, we prove that the density is bounded from above independently of time, consequently, it converges to the steady state density in Lp and the velocity u converges to the steady state velocity in W1,p for any 1p<∞ as time goes to infinity; furthermore, we show that if the initial density contains vacuum at least at one point, then the derivatives of the density must blow up as time goes to infinity. 相似文献
20.
Hongfang Ma 《Journal of Mathematical Analysis and Applications》2010,370(2):511-529
In this work, we study the 1-D isentropic bipolar hydrodynamic model. This model takes the form of compressible Euler-Poisson system with nonlinear damping added to the momentum equations. Under some smallness conditions, the solutions to the Cauchy problem of the system globally exist and convergence to the nonlinear diffusion waves, which are the corresponding solutions of nonlinear parabolic equations given by the Darcy's law with a specified initial data. The optimal convergence rates are obtained by Green function method when the initial perturbation is in L1-space. 相似文献