The Navier-Stokes equations in the weak- $L^n$ space with time-dependent external force
The Navier-Stokes equations in the weak- $L^n$ space with time-dependent external force
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DOI：
10.1007/pl00004418
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发表时间：
2000-08
影响因子：
1.4
通讯作者：
M. Yamazaki
中科院分区：
文献类型：
--
作者：
M. Yamazaki
摘要：本文考虑了具有含时外力的Navier-Stokes方程，无论是在全时还是在正时，初始值为零，区域为全空间、半空间或外维区域.在弱空间中，给出了在外力作用下小解唯一存在的充分条件。特别地，该结果给出了小时间周期解或概周期解的唯一存在性和稳定性的充分条件。这一结果推广了前人关于在外力与时间无关的弱空间中小定态解的存在唯一性和稳定性的结果。
Abstract.We consider the Navier-Stokes equations with time-dependent external force, either in the whole time or in positive time with initial data, with domain either the whole space, the half space or an exterior domain of dimension. We give conditions on the external force sufficient for the unique existence of small solutions in the weak-space bounded for all time. In particular, this result gives sufficient conditions for the unique existence and the stability of small time-periodic solutions or almost periodic solutions. This result generalizes the previous result on the unique existence and the stability of small stationary solutions in the weak-space with time-independent external force.