Stoxes方程初边值问题的Phragmén－Lindelöf二择性原理<sup>*</sup>

Stoxes方程初边值问题的Phragmén－Lindelöf二择性原理^*

基金项目: *国家自然科学基金;中山大学基金

摘要: 本文对非定常的Stokes方程的初边值问题证明了Phragmén-Lindelöf二择性原理,即证明Stokes流函数的能量,随着与带状区域有限端距离的增加必定或者按指数率增长或者按指数率衰减.对能量衰减情况建立了Stokes流速度的最大模的点点估计.并提出求全能量上界的方法.
- Stokes方程 /
- 初边值问题 /
- Phragmén－Lindelöf二择性原理 /
- 能量耗散估计
Abstract: In this paper we prove Phragmén-Lindelöf type alternative for the initial boundary problem of Stokes equation,i.e.we show that the energy expression for the solutionof the initial boundary problem must either grow exponentially or decay exponentially wilh axial distance from the end of a semi-infinite strip.For the case of decay,we alsoestablish the pointwise estimate for the maximum module of the Stokes flow and present a method for obtaining explicit bounds for the total energy.
- Stokes equation /
- initial boundary problem /
- phragmen-Lindelöf alternative theorem /
- estimate of energy dissipation

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