论文标题
关于流体 - 刚体相互作用问题的弱解决方案的规律性
On the regularity of weak solutions to the fluid-rigid body interaction problem
论文作者
论文摘要
我们研究3D液体 - 刚性体相互作用问题。流体流由3D不可压缩的Navier-Stokes方程控制，而刚体的运动由一个普通微分方程的系统描述，该系统描述了线性和角动量的保护。我们的目的是证明满足某些规律性条件的任何弱解决方案都是光滑的。这是对$ 3D $不可压缩的Navier-Stokes方程的经典结果的概括，该方程式说明，另外满足prodi-serrin $ l^r^r-l^s $条件的弱解决方案是平稳的。我们表明，在流体 - 刚体的情况下，生产 - 锯齿蛋白的条件表示分别针对流体速度和流体压力的$ w^{2，p} $和$ w^{1，p} $。此外，我们表明解决方案为$ c^{\ infty} $，如果另外，我们假设刚体的加速度几乎在任何地方变量都受到界限。
We study a 3D fluid-rigid body interaction problem. The fluid flow is governed by 3D incompressible Navier-Stokes equations, while the motion of the rigid body is described by a system of ordinary differential equations describing conservation of linear and angular momentum. Our aim is to prove that any weak solution satisfying certain regularity conditions is smooth. This is a generalization of the classical result for the $3D$ incompressible Navier-Stokes equations, which says that a weak solution that additionally satisfy Prodi - Serrin $L^r-L^s$ condition is smooth. We show that in the case of fluid - rigid body the Prodi - Serrin conditions imply $W^{2,p}$ and $W^{1,p}$ regularity for the fluid velocity and fluid pressure, respectively. Moreover, we show that solutions are $C^{\infty}$ if additionally we assume that the rigid body acceleration is bounded almost anywhere in time variable.
