论文标题
对于大型初始数据
Unbounded-energy solutions to the fluid+disk system and long-time behavior for large initial data
论文作者
论文摘要
在本文中，我们分析了解决方案对耦合系统的长期行为，该系统描述了2D粘性不可压缩的流体中刚性磁盘的运动。遵循以前的方法，我们研究与磁盘中心相关的坐标系统中的问题。这样做，我们向经典的Navier Stokes方程引入了进一步的非线性。与经典的非线性相比，这个新术语缺乏时间和空间的整合性，从而使对解决方案的长期行为的分析变得更加复杂。我们在此提供了两个精致的工具：对Gagliardo-Nirenberg不平等现象的精致分析，以及对所谓流体结构操作员的分数力量的透彻描述。在这两个工具的基础上，我们将先前的衰减估计值扩展到任意初始数据，并显示羔羊 - 俄e涡的局部稳定性。
In this paper, we analyse the long-time behavior of solutions to a coupled system describing the motion of a rigid disk in a 2D viscous incompressible fluid. Following previous approaches, we look at the problem in the system of coordinates associated with the center of mass of the disk. Doing so, we introduce a further nonlinearity to the classical Navier Stokes equations. In comparison with the classical nonlinearities, this new term lacks time and space integrability, thus complicating strongly the analysis of the long-time behavior of solutions. We provide herein two refined tools : a refined analysis of the Gagliardo-Nirenberg inequalities and a thorough description of fractional powers of the so-called fluid-structure operator. On the basis of these two tools we extend previous decay estimates to arbitrary initial data and show local stability of the Lamb-Oseen vortex.
