Well-Posedness for the Motion of Physical Vacuum of the Three-dimensional Compressible Euler Equations with or without Self-Gravitation
Well-Posedness for the Motion of Physical Vacuum of the Three-dimensional Compressible Euler Equations with or without Self-Gravitation
复制标题
DOI：
10.1007/s00205-014-0742-0
复制
发表时间：
2014-04
影响因子：
2.5
通讯作者：
T. Luo;Z. Xin;Huihui Zeng
中科院分区：
文献类型：
--
作者：
T. Luo;Z. Xin;Huihui Zeng
本文讨论了有无自引力作用下可压缩欧拉方程在物理真空中运动的适定性理论。首先证明了三维一般运动经典解的一般唯一性定理。第二，对于球对称运动，在不施加一阶导数在对称中心为零的相容条件的情况下，在包含比在（Coutand et al.，Commun Math Phys 296：559-587，2010; Coutand和Shkoller，Arch Ration Mech Anal 206：515-616，2012; Jang和Masmoudi，Well-posedness of compressable Euler equations in a physical vacuum，2008），通过构建合适的权重和截止函数，其特征在于对称中心和移动真空边界附近的解的行为。
This paper concerns the well-posedness theory of the motion of a physical vacuum for the compressible Euler equations with or without self-gravitation. First, a general uniqueness theorem of classical solutions is proved for the three dimensional general motion. Second, for the spherically symmetric motions, without imposing the compatibility condition of the first derivative being zero at the center of symmetry, a new local-in-time existence theory is established in a functional space involving less derivatives than those constructed for three-dimensional motions in (Coutand et al., Commun Math Phys 296:559–587, 2010; Coutand and Shkoller, Arch Ration Mech Anal 206:515–616, 2012; Jang and Masmoudi, Well-posedness of compressible Euler equations in a physical vacuum, 2008) by constructing suitable weights and cutoff functions featuring the behavior of solutions near both the center of the symmetry and the moving vacuum boundary.