On the Existence and Stability of Time Periodic Solution to the Compressible Navier–Stokes Equation on the Whole Space
On the Existence and Stability of Time Periodic Solution to the Compressible Navier–Stokes Equation on the Whole Space
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DOI：
10.1007/s00205-015-0902-x
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发表时间：
2014-09
影响因子：
2.5
通讯作者：
Kazuyuki Tsuda
中科院分区：
文献类型：
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作者：
Kazuyuki Tsuda
当空间维数大于或等于3时，对于一个足够小的时间周期外力，证明了可压缩Navier-Stokes方程在整个空间上的时间周期解的存在性.证明是基于在某些加权L ∞和Sobolev空间中与定常密度静止状态的线性化问题相关的时间-T-映射的谱性质。在充分小的初始扰动下，时间周期解是渐近稳定的，且扰动的L ∞范数随着时间的推移而衰减.
The existence of a time periodic solution of the compressible Navier–Stokes equation on the whole space is proved for a sufficiently small time periodic external force when the space dimension is greater than or equal to 3. The proof is based on the spectral properties of the time-T-map associated with the linearized problem around the motionless state with constant density in some weightedL∞and Sobolev spaces. The time periodic solution is shown to be asymptotically stable under sufficiently small initial perturbations and theL∞norm of the perturbation decays as time goes to infinity.