Rotating Fluids with Self-Gravitation in Bounded Domains
Rotating Fluids with Self-Gravitation in Bounded Domains
复制标题
DOI：
10.1007/s00205-004-0319-4
复制
发表时间：
2004-05
影响因子：
2.5
通讯作者：
T. Luo;J. Smoller
中科院分区：
文献类型：
--
作者：
T. Luo;J. Smoller
本文研究了有界区域上具有给定角速度的Euler-Poisson方程的定常解。该模型模拟了由可压缩理想流体组成的旋转牛顿星星，其状态方程为P =eSργ。当区域为球且角速度为常数时，我们得到了依赖于绝热气体常数γ的存在性和不存在性定理。此外，我们得到了一些有趣的性质的解决方案;例如，星星半径与角速度和中心密度的单调性。我们还证明了旋转球对称星星的半径，具有恒定的角速度和恒定的熵，是一致有界的中心密度无关。这在物理上是惊人的，与非旋转星星的情况形成鲜明对比。对于一般区域和变角速度情形，得到了等熵状态方程的存在性结果和非等熵状态方程的不存在性结果。
In this paper, we study the steady solutions of Euler-Poisson equations in bounded domains with prescribed angular velocity. This models a rotating Newtonian star consisting of a compressible perfect fluid with given equation of stateP=eSργ. When the domain is a ball and the angular velocity is constant, we obtain both existence and non-existence theorems, depending on the adiabatic gas constantγ. In addition we obtain some interesting properties of the solutions; e.g., monotonicity of the radius of the star with both angular velocity and central density. We 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 physically striking and in sharp contrast to the case of the non-rotating star. For general domains and variable angular velocities, both an existence result for the isentropic equations of state and non-existence result for the non-isentropic equation of state are also obtained.