Navier–Stokes equations in aperture domains: Global existence with bounded flux and time‐periodic solutions
Navier–Stokes equations in aperture domains: Global existence with bounded flux and time‐periodic solutions
复制标题
孔径域中的纳维-斯托克斯方程：具有有界通量和时间周期解的全局存在
DOI：
10.1002/mma.903
复制
发表时间：
2008
影响因子：
2.9
通讯作者：
P. Maremonti
中科院分区：
文献类型：
--
作者：
F. Crispo;P. Maremonti
我们考虑三维欧几里德空间的孔径域中的纳维-斯托克斯方程。我们有兴趣证明与小初始数据和通过孔径的通量相对应的常规解的存在。假设通量是平滑的并且有界于 (0, +∞)。因此，我们证明了与通过孔径的时间周期通量相对应的时间周期解的存在。最后，我们将我们的解决方案与属于更广泛类别的解决方案进行比较，表明如果确实存在这样的解决方案，则这两个解决方案是一致的。版权所有 © 2007 约翰·威利父子有限公司
We consider the Navier–Stokes equations in an aperture domain of the three‐dimensional Euclidean space. We are interested in proving the existence of regular solutions corresponding to small initial data and flux through the aperture. The flux is assumed to be smooth and bounded on (0, +∞). As a consequence, we prove the existence of a time‐periodic solution corresponding to a time‐periodic flux through the aperture. Finally, we compare our solution with a solution belonging to a wider class, showing that, if such a solution does exist, then the two solutions coincide. Copyright © 2007 John Wiley & Sons, Ltd.