Existence and Non-linear Stability of Rotating Star Solutions of the Compressible Euler–Poisson Equations
Existence and Non-linear Stability of Rotating Star Solutions of the Compressible Euler–Poisson Equations
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DOI：
10.1007/s00205-007-0108-y
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发表时间：
2007-03
影响因子：
2.5
通讯作者：
T. Luo;J. Smoller
中科院分区：
文献类型：
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作者：
T. Luo;J. Smoller
证明了在给定角动量和总质量的情况下，三维空间中可压缩等熵Euler-Poisson（Euler-Poisson）方程的旋转星星解的存在性.这个问题可以制定为一个变分问题，找到一个最小的能量泛函在一个更广泛的一类功能，具有较少的对称性比那些功能中考虑的经典Auchmuty-Beals文件。我们证明了这些解的非线性动力学稳定性与扰动具有相同的总质量和对称性的旋转星星解决方案。我们还证明了当扰动为Euler-Poisson方程的熵弱解时解的有限时间稳定性。最后，我们给出了Euler-Poisson方程熵弱解的一致先验估计。
We prove the existence of rotating star solutions which are steady-state solutions of the compressible isentropic Euler–Poisson (Euler–Poisson) equations in three spatial dimensions with prescribed angular momentum and total mass. This problem can be formulated as a variational problem of finding a minimizer of an energy functional in a broader class of functions having less symmetry than those functions considered in the classical Auchmuty–Beals paper. We prove the non-linear dynamical stability of these solutions with perturbations having the same total mass and symmetry as the rotating star solution. We also prove finite time stability ofsolutions where the perturbations are entropy-weak solutions of the Euler–Poisson equations. Finally, we give a uniform (in time) a priori estimate for entropy-weak solutions of the Euler–Poisson equations.