Well posedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid
Well posedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid
复制标题
模拟不可压缩粘性流体中任意形式刚体运动的系统的适定性
DOI：
10.1007/s10587-008-0063-2
复制
发表时间：
2008
影响因子：
0.5
通讯作者：
Takéo Takahashi
中科院分区：
文献类型：
--
作者：
Patricio Cumsille;Takéo Takahashi
在本文中，我们考虑刚体和不可压缩的均匀粘性流体之间的相互作用。假设该流固系统填充整个空间 ℝd，d = 2 或 3。流体方程是经典的纳维-斯托克斯方程，而刚体的运动受线性动量和角动量的标准守恒定律控制。流体域的时间变化（由于刚体的运动）是先验未知的，因此我们处理自由边值问题。我们通过证明完全适定性结果来改进已知结果：我们的主要结果产生了 d = 2 或 3 的强解的局部时间存在性和唯一性。此外，我们证明了该解对于 d = 2 以及 d = 3（如果数据足够小）在时间上是全局的。
In this paper, we consider the interaction between a rigid body and an incompressible, homogeneous, viscous fluid. This fluid-solid system is assumed to fill the whole space ℝd, d = 2 or 3. The equations for the fluid are the classical Navier-Stokes equations whereas the motion of the rigid body is governed by the standard conservation laws of linear and angular momentum. The time variation of the fluid domain (due to the motion of the rigid body) is not known a priori, so we deal with a free boundary value problem.We improve the known results by proving a complete wellposedness result: our main result yields a local in time existence and uniqueness of strong solutions for d = 2 or 3. Moreover, we prove that the solution is global in time for d = 2 and also for d = 3 if the data are small enough.