论文标题
三维粘性不可压缩的液体中刚体的消失极限
The vanishing limit of a rigid body in three-dimensional viscous incompressible fluid
论文作者
论文摘要
我们考虑一个小刚体在不可压缩的粘性液中的演变，填充了整个空间$ \ rline^3 $。当小刚体从密度恒定的意义上缩小到“无质量”点时，我们证明流体 - 刚性身体系统的溶液会收敛到整个空间中Navier-Stokes方程的溶液。基于流体结构半群的一些$ l^p-l^q $估计值和固定点论点，我们获得了刚体速度的统一估计。这使我们能够构建可允许的测试功能，该功能在传递到极限的过程中起着关键作用。
We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space $\rline^3$. When the small rigid body shrinks to a "massless" point in the sense that its density is constant, we prove that the solution of the fluid-rigid body system converges to a solution of the Navier-Stokes equations in the full space. Based on some $L^p-L^q$ estimates of the fluid-structure semigroup and a fixed point argument, we obtain a uniform estimate of velocity of the rigid body. This allows us to construct admissible test functions which plays a key role in the procedure of passing to the limit.
