论文标题
动态障碍物振荡引起的时间周期性的Navier-Stokes流动的空间行为
Spatial pointwise behavior of time-periodic Navier-Stokes flow induced by oscillation of a moving obstacle
论文作者
论文摘要
我们研究以$ | x |^{ - 1} $在3D外部域中的速率$ | x |^{ - 1} $流动的空间衰减，当刚体定期及时移动时。在这种制度中，Galdi和Silvestre在2006年的论文中首先建立了时间周期性解决方案，但是，关于无穷大的空间行为的信息很少，因此无法提供解决方案的唯一性。 Galdi已经解决了后一个问题，Galdi最近成功地构建了独特的时间周期性解决方案，并在上面提到的空间行为，如果身体的翻译和角度速度达到了，除了小小的和规律性，以下是以下假设：（i）不存在翻译或旋转； （ii）两个速度平行于相同的常数矢量。本文显示了在弱$ l^3 $空间中的值中存在独特的时间周期性的Navier-Stokes流动，然后在某种情况下在某种情况下在身体的刚体运动中推断出所需的溶液的尖锐衰减，涵盖了上述情况（i），（II），（II），（II）。
We study the spatial decay of time-periodic Navier-Stokes flow at the rate $|x|^{-1}$ with/without wake structure in 3D exterior domains when a rigid body moves periodically in time. In this regime the existence of time-periodic solutions was established first in the 2006 paper by Galdi and Silvestre, however, with little information about spatial behavior at infinity so that uniqueness of solutions was not available. This latter issue has been addressed by Galdi, who has recently succeeded in construction of a unique time-periodic solution with spatial behavior mentioned above if translational and angular velocities of the body fulfill, besides smallness and regularity, either of the following assumptions: (i) translation or rotation is absent; (ii) both velocities are parallel to the same constant vector. This paper shows the existence of a unique time-periodic Navier-stokes flow in the small with values in the weak-$L^3$ space and then deduces the desired pointwise decay of the solution under some condition on the rigid motion of the body, that covers the cases (i), (ii) mentioned above.
