Existence of non-steady flows of an incompressible, viscous drop of fluid in a frame rotating with finite angular velocity
Existence of non-steady flows of an incompressible, viscous drop of fluid in a frame rotating with finite angular velocity
复制标题
以有限角速度旋转的框架中不可压缩的粘性液滴的非稳态流动的存在
DOI：
10.1142/9789812777201_0019
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
V. Solonnikov
中科院分区：
文献类型：
--
作者：
M. Padula;V. Solonnikov
本文给出了一个关于不可压缩粘性流体流动的Navier-Stokes方程整体非定常解的存在性定理。具体来说，我们证明，在表面张力的存在下，如果一个刚性旋转承认一个稳定的配置在毛细理论的意义上，然后任何适当的小初始扰动的形状和速度场存在一个唯一的全球非稳态解，最终去稳定的刚性旋转，随着时间的推移到无穷大，指数衰减率。我们的证明是基于文献[13]证明的局部正则解的存在性定理，以及文献[7]中关于解的先验估计，即解的弱范数在时间上是一致的.结果并不假设液滴的角速度很小，而只是假设初始数据很小！
We give an existence theorem of global non-steady solutions of the Navier-Stokes equations governing flows of a incompressible viscous fluid totally bounded by free surface. Specifically, we prove that, in the presence of surface tension, if a rigid rotation admits a stable configuration in the sense of capillarity theory, then to any suitably small initial perturbation to the shape and to the velocity field there exists a unique global non-steady solution which eventually goes to the stable rigid rotation as time goes to infinity, with exponential decay rate. Our proof is based on a existence theorem of local regular solutions proved by [13], and on some a priori estimates on the solution, uniform in time for weak norms of the solution in the wake of [7]. The result does not assume smallness on angular velocity of the drop, only smallness on initial data!.