On Spherically Symmetric Motions of the Atmosphere Surrounding a Planet Governed by the Compressible Euler Equations
On Spherically Symmetric Motions of the Atmosphere Surrounding a Planet Governed by the Compressible Euler Equations
复制标题
关于由可压缩欧拉方程控制的行星周围大气的球对称运动
DOI：
10.1619/fesi.58.43
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
T. Makino
中科院分区：
文献类型：
--
作者：
T. Makino
我们考虑在地心引力作用下，无粘可压缩气体围绕一个实心球的球对称运动。平衡点以有限半径接触真空，其中一个平衡点周围的线性化方程具有时间周期解。为了证明线性化，我们应该构造真正的解，这个时间周期解加上平衡是第一近似。但这给我们带来了由自由边界上与真空接触的奇点所引起的困难。我们用纳什-莫泽定理来解决这个问题。
We consider spherically symmetric motions of inviscid compressible gas surrounding a solid ball under the gravity of the core. Equilibria touch the vacuum with finite radii, and the linearized equation around one of the equilibria has time-periodic solutions. To justify the linearization, we should construct true solutions for which this time-periodic solution plus the equilibrium is the first approximation. But this leads us to difficulty caused by singularities at the free boundary touching the vacuum. We solve this problem by the Nash-Moser theorem.