Title: On the regularity of weak solutions to time-periodic Navier--Stokes equations in exterior domains Show Chinese title

Title: 关于外区域中时间周期性纳维-斯托克斯方程弱解的正则性

Abstract: 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. Show Chinese abstract

Abstract: 考虑无限远处具有非零速度的周期性时间粘性不可压缩流体绕物体的流动。 本文给出了充分条件，使得该问题的弱解是光滑的。 由于一般情况下周期性解没有有限的动能，因此对应初值问题的弱解的著名正则性结果不能直接转移。 建立的正则性准则要求速度场或其梯度的纯周期部分具有一定的可积性，但不涉及这些量的时间平均值。