论文标题
关于时间周期性纳维尔的弱解决方案的规律性 - 外部域中的stokes方程
On the regularity of weak solutions to time-periodic Navier--Stokes equations in exterior domains
论文作者
论文摘要
考虑时间周期性粘性不可压缩的流体流，经过无数速度的体内的体。本文提供了足够的条件，因此解决此问题的薄弱解决方案是顺畅的。由于时间周期溶液通常没有有限的动能，因此无法直接传输相应初始问题的弱解的众所周知的规律性结果。既定的规律标准要求速度领域的纯粹周期性部分或其梯度的一定的整合性，但它并不涉及这些数量的时间平均值。
Consider the time-periodic viscous incompressible fluid flow past a body with non-zero velocity at infinity. This article gives sufficient conditions such that weak solutions to this problem are smooth. Since time-periodic solutions do not have finite kinetic energy in general, the well-known regularity results for weak solutions to the corresponding initial-value problem cannot be transferred directly. The established regularity criterion demands a certain integrability of the purely periodic part of the velocity field or its gradient, but it does not concern the time mean of these quantities.
