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首页> 外文期刊>Journal of Mathematical Analysis and Applications >Blowup for the C~1 solutions of the Euler-Poisson equations of gaseous stars in R~N
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Blowup for the C~1 solutions of the Euler-Poisson equations of gaseous stars in R~N

机译：R〜N中气态恒星Euler-Poisson方程C〜1解的爆破

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摘要

The Newtonian Euler-Poisson equations with attractive forces are the classical models for the evolution of gaseous stars and galaxies in astrophysics. In this paper, we use the integration method to study the blowup problem of the N-dimensional system with adiabatic exponent γ>1, in radial symmetry. We could show that the C1 non-trivial classical solutions (ρ,V), with compact support in [0,R], where R>0 is a positive constant with ρ(t,r)=0 and V(t,r)=0 for r≥R, under the initial condition. with an arbitrary constant n>max(N-2,0) and the total mass M, blow up before a finite time T for pressureless fluids or γ>1. Our results could fill some gaps about the blowup phenomena to the classical C1 solutions of that attractive system with pressure under the first boundary condition. In addition, the corresponding result for the repulsive systems is also provided. Here our result fully covers the previous case for n=1 in [M.W. Yuen, Blowup for the Euler and Euler-Poisson equations with repulsive forces, Nonlinear Anal. 74 (2011) 1465-1470].
机译：具有吸引力的牛顿欧拉-泊松方程是天体物理学中气态恒星和星系演化的经典模型。本文采用积分法研究了绝热指数为γ> 1的N维系统的径向对称爆炸问题。我们可以证明C1非平凡经典解（ρ，V）在[0，R]中具有紧致支持，其中R> 0是一个正常数，其中ρ（t，r）= 0且V（t，r在初始条件下，对于r≥R，）= 0。对于任意压力的流体，或者在γ> 1的情况下，在一个有限的时间T之前将任意常数n> max（N-2,0）和总质量M炸开。我们的结果可能会填补在第一个边界条件下具有吸引力的经典C1解的爆破现象的空白。此外，还提供了排斥系统的相应结果。在这里，我们的结果完全覆盖了[M.W. Yuen，带有排斥力的Euler和Euler-Poisson方程的爆破，非线性分析。 74（2011）1465-1470]。

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